In the Anglican tradition, the prayer for calling down the Holy Ghost upon the elements to hallow and bless them is termed "the Invocation", very sensibly, since this is the more immediately comprehensible Latinate term for the Epiclesis (its exact Greek equivalent and antecedent term).
[In discussing this area of Eucharistic theology, I prescind here from the question of whether Anglicans can in fact consecrate the Sacrament at all - though of course I accept the decision of Pope Leo XIII in Apostolicæ curæ.]
A good consecratory Invocation properly prays for the transsubstantiation of the bread and wine, that they may "become" (fiant) the Body and Blood of Christ. Since this is for our sake, that this Sacrament and Sacrifice impart to us life and all the unspeakable, ineffable benefits of His Passion, the liturgy - as in the Roman Canon - prays that the bread and wine "become for us" (fiant nobis) His Body, His Blood. But all subjective, nominalist interpretation must be excluded: it is not that they "become" Christ's Flesh and Blood only in sign or figure or from our perspective; no, they truly change in their very natural substances, objectively ceasing to be bread and wine, in such manner that in every sense they are made the Body and the Blood of the Lord, only their outward perceptible appearances of bread and wine remaining unchanged.
Therefore, a petition that "this bread and wine may be for us the Body and Blood of Christ" is gravely suspect - it seems to imply that no objective change takes place, but that they simply serve to represent His Flesh, His Blood. This would be the error of transsignification or transfinalization: as if the bread and wine now signify His Body and Blood, or that they no longer have the natural purpose of feeding us, but are empowered with a new final causality, to impart to us Christ's life. This is insufficient, and the Holy Catholic Church in her solemn teaching reprobates and rejects such heresies.
Worse still would be an epicletic or invocatory prayer that prays "that we, receiving this bread and wine, may partake of Christ's Body and Blood" - for that would be an expression of the damnable falsity that is receptionism, Hooker's new heresy, according to which the bread and wine change not at all, but that, at the moment of partaking of them, their eaters and drinkers mystically and sacramentally eat and drink Christ. This is not far from Cranmer's Zwinglian madness.
Unfortunately, the Anglican Books of Common Prayer largely contain heterodox Epicleses.
It was the glory of the Scottish Episcopalians (whom I'm told have in past decades utterly gone to the dogs, their High Church doctrine having been vitiated by the acceptance of moral turpitude) that their eighteenth century Divines, following the English Nonjurors with whom they were in communion, and accepting the Patristic era testimony of the documents known as the Apostolic Constitutions, improved the text of the Invocation in their liturgies.
From them descend the U.S. Episcopalians - nowadays also turned liberal modernist heretics of the worst odour - but their liturgies reverted to the older Anglican type, by almost immediately abandoning the full-blooded Scottish epicletic prayer in favour of the receptionist English form. Only their very first provisional liturgy, that of Bp Seabury, had a proper epiclesis - for he had obtained Anglican episcopal consecration from the Scottish Episcopalians on condition that he adopt and promote their form of worship in the nascent United States' Episcopal Church; he succeeded only partly, and lost out on the matter of this prayer.
Here - in descending order of orthodoxy - are Seabury's epiclesis, equivalent to the 1764 Scottish form ("become"), then that of the 1637 Scottish ("may be unto us") - which combines the English 1549 and 1552 forms - and finally that of the 1928 U.S. B.C.P. ("that we receiving them"):
Bp Seabury's Communion Office (1786),equivalent to the Scottish 1764 Communion OfficeAnd we most humbly beseech thee, O merciful Father to hear us, and of thy almighty goodness vouchsafe to bless and sanctify, with thy word and Holy Spirit, these thy gifts and creatures of bread and wine, that they may become the body and blood of thy most dearly beloved Son.Scottish 1637 B.C.P.Hear us, merciful Father, we most humbly beseech thee, and of thy almighty goodness vouchsafe so to bless and sanctify with thy word and holy Spirit these thy gifts and creatures of bread and wine, that they may be unto us the body and blood of thy most dearly beloved Son; so that we receiving them according to thy Son our Saviour Jesus Christs holy institution, in remembrance of his death and passion, may be partakers of the same his most precious body and blood.U.S. 1928 B.C.P.And we most humbly beseech thee, O merciful Father, to hear us; and, of thy almighty goodness, vouchsafe to bless and sanctify, with thy Word and Holy Spirit, these thy gifts and creatures of bread and wine; that we, receiving them according to thy Son our Saviour Jesus Christ’s holy institution, in remembrance of his death and passion, may be partakers of his most blessed Body and Blood.