Reformed and Catholic Eucharist...

The Reformed tradition accepts the four councils of Nicea,  Constantinople, Ephesus 1, and Chalcedon.  In his 1559 edition of Institutes of the Christian Religion, John Calvin wrote:

… we willingly embrace and reverence as holy the early councils, such as those of Nicaea, Constantinople, Ephesus I, Chalcedon, and the like, which were concerned with refuting errors-in so far as they relate to the teachings of faith. For they contain nothing but the pure and genuine exposition of Scripture, which the holy fathers applied with spiritual prudence to crush the enemies of religion who had then arisen.

The ecumenical council at Ephesus in 431, regarding the Lord's Supper, stated in part:

Proclaiming the death according to the flesh of the only begotten Son of God, that is Jesus Christ, and professing his return to life from the dead and his ascension into heaven, we offer the unbloody sacrifice in the churches and so proceed to the mystical thanksgivings and are sanctified having partaken of the holy flesh and precious blood of Christ, the saviour of us all. This we receive not as ordinary flesh, heaven forbid, nor as that of a man who has been made holy and joined to the Word by union of honor, or who had a divine indwelling, but as truly the life-giving and real flesh of the Word. For being life by nature as God, when he became one with his own flesh, he made it also to be life-giving, as also he said to us [in John 6:52]: “Amen I say to you, unless you eat the flesh of the Son of man and drink his blood” .

Roman Catholics read transubstantiation and a misunderstanding of “sacrifice” into the Ephesus 431 quote and thereby judge that Reformed Protestant worship is not catholic, i.e. that the Reformed churches reject the council's teaching.  But that is not the case.  Looking to the Church of England’s Holy Communion service as found in the 1662 BCP (still in use) to help clarify the right understanding of this mystery one finds:

WE do not presume to come to this thy Table, O merciful Lord, trusting in our own righteousness, but in thy manifold and great mercies. We are not worthy so much as to gather up the crumbs under thy Table. But thou art the same Lord, whose property is always to have mercy: Grant us therefore, gracious Lord, so to eat the flesh of thy dear Son Jesus Christ, and to drink his blood, that our sinful bodies may be made clean by his body, and our souls washed through his most precious blood, and that we may evermore dwell in him, and he in us. Amen.

THE Body of our Lord Jesus Christ, which was given for thee, preserve thy body and soul unto everlasting life. Take and eat this in remembrance that Christ died for thee, and feed on him in thy heart by faith with thanksgiving.

THE Blood of our Lord Jesus Christ, which was shed for thee, preserve thy body and soul unto everlasting life. Drink this in remembrance that Christ’s Blood was shed for thee, and be thankful.

The Reformed confession of the Church of England further explains the nature of the sacrament: 
 The Thirty-Nine Articles of Religion; Art. 28:

THE Supper of the Lord is not only a sign of the love that Christians ought to have among themselves, one to another, but rather it is a sacrament of our redemption by Christ’s death: insomuch that to such as rightly, worthily, and with faith receive the same, the bread which we break is a partaking of the body of Christ, and likewise the cup of blessing is a partaking of the blood of Christ.
Transubstantiation (or the change of the substance of bread and wine) in the Supper of the Lord, cannot be proved by Holy Writ, but is repugnant to the plain words of Scripture, overthroweth the nature of a Sacrament, and hath given occasion to many superstitions.
The body of Christ is given, taken, and eaten in the Supper, only after an heavenly and spiritual manner. And the mean whereby the body of Christ is received and eaten in the Supper is Faith.

 The Sacrament of the Lord’s Supper was not by Christ’s ordinance reserved, carried, about, lifted up, or worshipped.

  
My reading of the Ephesus Council quote:

We “offer the unbloody sacrifice in the churches…” i.e. the Sacrament of the Supper (which proclaims Christ’s sacrifice on the cross) is offered to the believers in the churches as real spiritual food for the soul’s nourishment. Note the word “unbloody”, i.e. not corporeal blood. In the same way, in preaching the Gospel, the “sacrifice of Christ is offered” for forgiveness of sins to all that hear it and believe.

This we receive not as ordinary flesh, heaven forbid, nor as that of a man who has been made holy and joined to the Word by union of honor, or who had a divine indwelling, but as truly the life-giving and real flesh of the Word.

Note: “not as ordinary flesh”… in other words not actual physical flesh as one ordinarily would understand… “heaven forbid” i.e. put away the thought that this is physical flesh of a real man, even one “joined to the Word by union of honor.”

Jesus explains to his disciples after their confusion and the objections raised by many of the listens to the words of John 6:52 quoted in Ephesus 431:

61 But Jesus knowing in himself that his disciples murmured at this, said unto them, Doth this cause you to stumble?
62 What then if ye should behold the Son of man ascending where he was before?
63 It is the spirit that giveth life; the flesh profiteth nothing: the words that I have spoken unto you are spirit, are are life.

Thus we receive the body and blood of Christ in the Supper by faith “only after an heavenly and spiritual manner.” (39 Articles. 28)

The only sacrifice offered to God by the clergy or the people is expressed in the final prayer of the Holy Communion in the 1662 BCP service:

“O LORD and heavenly Father, we thy humble servants entirely desire thy fatherly goodness mercifully to accept this our sacrifice of praise and thanksgiving; most humbly beseeching thee to grant, that by the merits and death of thy Son Jesus Christ, and through faith in his blood, we and all thy whole Church may obtain remission of our sins, and all other benefits of his passion. And here we offer and present unto thee, O Lord, ourselves, our souls and bodies, to be a reasonable, holy, and lively sacrifice unto thee; humbly beseeching thee, that all we, who are partakers of this holy Communion, may be fulfilled with thy grace and heavenly benediction. And although we be unworthy, through our manifold sins, to offer unto thee any sacrifice, yet we beseech thee to accept this our bounden duty and service; not weighing our merits, but pardoning our offences, through Jesus Christ our Lord; by whom, and with whom, in the unity of the Holy Ghost, all honour and glory be unto thee, O Father Almighty, world without end. Amen.” 

See-Saw Reform: The Church of England's confused course...

The duck-billed platypus pictured here has been proposed by some as a sort of "patron" mascot of the Anglican Church, inasmuch as the odd looking creature is hard to define.  Bird, mammal, reptile?  Roman Catholic, Protestant, Orthodox?  By in large I appreciate the intent of the analogy, that being that there is nothing incompatible between that which is truly small 'c' Catholic and truly Protestant.  Yet I wonder if this depiction might, unfortunately, be apt for another reason:  that it's a metaphor for unresolved tensions in Anglicanism that have their origins in the 16th century reformation of the English Church.  What I'm referring to is the battle for the doctrinal soul of the Church of England that began with Thomas Cranmer becoming the Archbishop in 1533 and the subsequent years of reform and compromise in both doctrine and practice.

By the time of his appointment, Cranmer had already had come to accept the essential doctrines of the reformation.  Over the next several years he would leave behind the Roman Catholic doctrine of transubstantiation, as well as accepting only two sacraments (holy communion and baptism) as of the gospel and instituted by Christ.  The other five so-called sacraments (confession, marriage, confirmation, anointing of the sick, holy orders), though valid and godly in nature, were not biblically instituted as such nor had they two parts (outward material sign and inward grace) necessary for a sacrament.

Cranmer's reformed path was quite distinct from a large percentage of the bishops who served throughout England at that time.  Many of those men were still Roman Catholic in outlook, if not in doctrine and practice.  The years leading up to the death of King Henry VIII were marked by a kind of see-saw slow-motion reform... three steps forward, two steps back, so to speak.  This was clearly seen in the first attempt at a church confession, the Ten Articles, which was a compromise between the Roman Catholic party and those favoring  reform.  King Henry as monarch had become the Supreme Head of the Church when England threw off the Pope's authority.  As was his wont when deciding doctrinal questions, he selected the committee bishops by appointing equal representation from the Catholic conservatives and the evangelical reformers; the perfect formula for doctrine compromise based on a political consensus rather than Holy Scripture alone.

This was to be the pattern throughout the latter part of Henry's reign.  It reflected his own theological ambivalence and ever-changing political concerns.  This course set the stage for three developments that stayed with the English Church for the next 100-plus years of back and forth reform.  One, it unofficially institutionalized a doctrinal see-saw battle between the Evangelicals and those of the more Catholic/medieval persuasion.  Two, it validated a kind of rear-guard action by the Catholic conservative bishops (often in sync with the King or Queen)  to preserve or reinstate certain medieval doctrines and practices and resist a fuller reformation of the English Church.  Three, the involvement of the Monarch as both head of State and Church guaranteed that political calculations as well as personal religious preferences would intrude themselves in matters of Church doctrine, practice, and further reform.

Anglican Reformation Dissonance...

Yes, at present, I consider myself a reformed Christian of the Anglican persuasion, although I find little evidence of any reformed identification and understanding in any but the smallest outposts of Anglicanism.

It is a rather dismal reality for one who, later in life, came to the modern incarnation of the church of Thomas Cranmer only to find what one might label as a "truth-in-advertising" problem.  The clear teaching and nature of the Book of Common Prayer (especially 1662) and The Thirty-Nine Articles are (and the position of the 16th century English reformers was) reformed and small 'c' catholic.  Yet all too many Anglicans today recoil uncomfortably at the words reformed, Evangelical, and Protestant while embracing a more or less pre-Reformation understanding of catholicity.  A bit of historical dissonance?

For these Anglicans it’s as if the Reformation never really happened in England except for the throwing off some of the outward trappings of Rome, the papacy, and many of its medieval innovations.  It’s a view of the 16th century religious upheaval as one of purely negative renovations that fails to embrace the positive and necessary historical recovery of justification through faith alone in Christ alone by God’s grace alone and the ultimate authority of Scripture.  It’s a position that blanches at the idea that there was any substantial commonality between the Church of England reformation doctrines and that of the Continental reformers.  And it is for these reasons that there’s little to be heard of the proclamation of the glorious good news of God’s gracious salvation of man - the justification of the ungodly by faith alone in Christ - in the homilies and teachings from Anglican pulpits in the United States.  Michael Horton is right on the money when he says that today’s Christian church needs a modern reformation.  It is certainly the case for the Anglican tradition. And I have to think that Thomas Cranmer would agree.