The case for the Reformed/Calvinist roots of Anglicanism has been made by many Anglicans over the years; Augustus Toplady, J.C. Ryle, J.I. Packer to name a few. One can go back to primary sources such as the Thirty-Nine Articles of Religion which has always been included in the lists
of Reformed confessions along with the Westminster Standards and the Three Forms of Unity (Dordt, the Heidelberg Catechism, and the Belgic Confession). Unfortunately over the years the Thirty-Nine Articles of Religion has undergone a number of reinventions by those who wished and largely succeeded to move the Church of England and worldwide Anglicanism away from its early Calvinist connections towards a more broad church or Anglo-Catholic position. Well, this just doesn't stand up when actual history is brought into focus.
Continental historians, both Protestant and Catholic, rank the Church of England among the Reformed Churches as distinct from the Lutheran, and her Articles are found in every collection of Reformed Confessions... the theological interpretation of the Articles by English writers has been mostly conducted in a controversial rather than an historical spirit. (Philip Schaff as quoted by J.I. Packer in his book The Thirty-Nine Articles - Their Place and Use Today, p 33)
One can have their own interpretation of the Articles, but not their own history. As Packer notes in the same book, "it is crooked thinking when the case for redefining Anglicanism is presented as the verdict of Anglican history" (p 36).
Below is an extended excerpt from what is commonly referred to as Nowell's Catechism. The catechism teaches the theology of Anglicanism as it stood a mere 16 years after the martyrdom of Thomas Cranmer when it was officially adopted by the Church of England in 1572. It presents the Reformed teachings on justification and good works echoing Calvin as well as unpacking doctrines found in the Westminster Confession of Faith (esp. Chapter 11 - Of Justification and Chapter 16 - Of Good Works) sixty years before the Westminster Assembly met! Go figure...
Dive in. Carefully read and you'll find mainstream Reformed soteriology as held by Anglicanism in its earliest years.
From Nowell's Catechism:
Master: Now thou hast declared the Creed, that is the sum of the Christian faith, tell me, what profit get we of this faith?
Student: Righteousness before God, by which we are made.
Master: Doth not then our own godliness toward God, and leading of our life honestly and holily among men justify us before God?
Student: Of this we have said somewhat already after the declaring of the law, and in other places, to this effect. If any man were able to live uprightly according to the precise rule of the law of God, he should worthily be counted justified by his good works. But seeing we are all most far from that perfection of life, yea, and be so oppressed with conscience of our sins, we must take another course, and find another way, how God may receive us into favour, than by our own deserving.
Master: What way?
Student: We must flee to the mercy of God, whereby he freely embraceth us with love and goodwill in Christ, without any our deserving, or respect of works, both forgiving us our sins, and so giving us the righteousness of Christ by faith in him, that for the same Christ’s righteousness he so accepteth us, as if it were our own. To God’s mercy therefore through Christ we ought to impute all our justification .
Master: How do we know it to be thus?
Student: By the gospel, which containeth the promises of God by Christ, to the which when we adjoin faith, that is to say, an assured persuasion of mind and stedfast confidence of God’s goodwill, such as hath been set out in the whole Creed, we do, as it were, take state and possession of this justification that I speak of.
Master: Dost not thou then say that faith is the principal cause of this justification, so as by the merit of faith we are counted righteous before God?
Student: No; for that were to set faith in the place of Christ. But the spring-head of this justification is the mercy of God, which is conveyed to us by Christ, and is offered to us by the gospel, and received of us by faith as with a hand.
Master: Thou sayest then that faith is not the cause but the instrument of justification; for that it embraceth Christ which is our justification; coupling us with so strait bond to him, that it maketh us partakers of all his good things?
Student: Yea forsooth.
Master: But can this justification be so severed from good works, that he that hath it can want them?
Student: No: for by faith we receive Christ such as he delivereth himself unto us. But he doth not only set us at liberty from sins and death, and make us at one with God, but also with the divine inspiration and virtue of the Holy Ghost doth regenerate and newly form us to the endeavour of innocency and holiness, which we call newness of life.
Master: Thou sayest then that justice, faith, and good works, do naturally cleave thogether, and therefor ought no more to be severed, than Christ, the of them in us, can be severed from himself.
Student: It is true.
Master: Then this doctrine of faith doth not withdraw men's minds from godly works and duties?
Student: Nothing less. For good works do stand upon faith as upon their root. So far, therefore, is faith from withdrawing our hearts from living uprightly, that, contrariwise, it doth most vehemently stir us up to the endeavour of good life; yea and so far, that he is not truly faithful that doth not also to his power both shun vices and embrace virtues, so living always as one that looketh to give an account.
Master: Therefore tell me plainly how our works be acceptable to God, and what rewards be given to them?
Student: In good works, two things are principally required. First, that we do those works that are prescribed by the law of God; secondly, that they be done with that mind and faith which God requireth. For no doings or thoughts enterprised or conceived without faith can please God.
Master: Go forward.
Student: It is evident, therefore, that all works whatsoever we do, before that we be born again and renewed by the Spirit of God, such as may properly be called our own works are faulty. For whatsoever shew of brightness and worthiness they represent and give to the eyes of men, since they spring and proceed from a faulty and corrupted heart, which God chiefly considereth, they cannot but be defiled and corrupted, and so grievously offend God. Such works, therefore, as evil fruits, growing out of an evil tree, God despiseth and rejecteth from him.
Master: Can we not, therefore, go before God with any works or deservings, whereby we may first provoke him to love us, and be good unto us?
Student: Surely, with none. For Gos loved and chose us in Christ, not only when we were his enemies, that is, sinners, but also before the foundations of the world were laid. And this is the same spring-head and original of our justification, whereof I spake before.
Master: What thinkest thou of those works which we, after that we be reconciled to God's favour, do by the instinct of the Holy ghost?
Student: The dutiful works of godliness, which proceedeth out of faith, working be charity, are indeed acceptable to God, yet not by their own deserving; but for that he, of his liberality, vouchsafeth them his favour. For though they be derived from the Spirit of God, as little streams from the spring-head, yet of our flesh, that mingleth itself with them, in the doing by the way, they receive corruption, as it were by infection, like as a river, otherwise pure and clear, is troubled and mudded with mire and slime, wherethrough it runneth.
Master: How then dost thou say that they please God?
Student: It is faith that procureth God's favour to our works, while it is assured that he will not deal with us after extremity of law, nor call our doings to exact account, nor try them as it were by the square: that is, he will not, in valuing and weighing them use severity, but remitting and pardoning all their corruptness, for Christ's sake and his deservings, will account them for fully perfect.
Master: Then thou standest still in this, that we cannot by merit of works obtain to be justified before God, seeing thou thinkest that all doings of men, even the perfectest, do need pardon?
Student: God himself hath so decreed in his word; and his Holy Spirit doth teach us to pray that he bring us not into judgment. For where righteousness, such as God the Judge shall allow, ought to be throughly absolute, and in all parts and points fully perfect, such as is to be directed and tried by the most precise rule, and, as it were, by the plumb-line of God's law and judgment; and therefore our works, even the best of them, for that they swerve and differ most far from the rule and prescription of God's law and justice, are many ways to be blamed and condemned; we can in no wise be justified before God by works.
Master: Doth not this doctrine withdraw men's minds from the duties of godliness, and make them slacker and slower to good works, or at least less cheerful and ready to godly endeavours?
Student: No: for we may not therefore say that good works are unprofitable or done in vain and without cause, for that we obtain not justification by them. For they serve both to the profit of our neighbour and to the glory of God; and they do, as by certain testimonies, assure us of God's goodwill toward us, and of our love again to God-ward, and of our faith, and so consequently of our salvation. And the reason it is, that we being redeemed with the blood of Christ the Son of God, and having beside received innumerable and infinite benefits of God, should live and wholly frame ourselves after the will and appointment of our Redeemer, and so shew ourselves mindful and thankful to the Author of our salvation, and by our example procure and win other unto him. The man that calleth these thoughts to mind may sufficiently rejoice in his good endeavours and works.
Master: But God doth allure us to good doing with certain rewards, both in this life and in the life to come, and doth covenant with us as it were for certain wages.
Student: That reward, as I have said, is not given to our works for their worthiness, and rendered to them as recompence for deservings, but by the bountifulness of God is freely bestowed upon us without deserving. And justification God doth give us as a gift of his own dear love toward us, and of his liberality through Christ. When I speak of God's gift and liberality, I mean it free and bountiful, without any our desert or merit: that it be God's mere and sincere liberality, which he applieth to or salvation only whom he loveth and which trust in him, not hired or procured for wages, as it were a merchandise of his commodities and benefits used by him for some profit to himself, requiring again of us some recompence or price, which once to think were to abate both the liberality and majesty of God.
Master: Whereas then God doth by faith both give us justification, and by the same faith alloweth and accepteth our works, tell me, dost thou think that this faith is a quality of nature, or the gift of God?
Student: Faith is the gift of God, and a singular and excellent gift. For both our wits are too gross and dull to conceive and understand the wisdom of God, whose fountains are opened by faith, and our hearts are more apt either to distrust, or to wrongful and corrupt trust in ourselves, or in other creatures, than to true trust in God. But God, instructing us with his word and lightening our minds with his Holy Spirit, maketh us apt to learn those things that otherwise would be far from entering into the dull capacity of our wits; and sealing the promises of salvation in our souls, he so informeth us that we are most surely persuaded of the truth of them. These things the apostles understanding, do pray to increase their faith.
In short, I affirm, that not by our own merit but by faith alone, are both our persons and works justified [i.e. accepted]; and that the justification of works depends on the justification of the person, as the effect on the cause. (John Calvin, Acts of the Council of Trent with the Antidote)
See also this post: John Calvin: The Recompense of Good Works