Dear old Fortescue's The Mass records the long debates of liturgists a century ago about where the epiclesis of the Roman Rite originally was before it ... er ... "dropped out". Their assumption, of course, was that the epiclesis was original to Christian liturgy and that the Oriental rites which preserve it were more 'primitive' than the Roman Rite. Now, happily, we know better. We see the Oriental epiclesis as a comparatively late fad in the evolving liturgical tradition. Rather than seeking traces of a lost epiclesis in the Canon Romanus, we realise that the prayer Supplices te rogamus, in which we pray that our offerings be taken to the Heavenly Altar, represents an earlier and lovelier expression of the linkage between our offering and the eternal oblation of the Eternal Son at the Heavenly Altar. Patrimony liturgists such as E C Ratcliffe played a large role here, not to mention Dom Gregory.
There has been an unfortunate fashion among Anglican Committees, not only for inserting epicleses (they have even plopped the Holy spirit into Dr Cranmer's Consecration Prayer), but also for putting them after the Institution Narrative. This is partly due to the rather naive idea that it is terribly Sophisticated to avoid the notion of a Moment of Consecration*, and partly to the dislike among the resurgent Evangelical Party for any idea at all of Consecration (expressed also in rubrical provisions for the celebrant, if he realises he is running short of consecrated Elements, simply to add some more hosts to the ciborium without saying anything). Evangelicals, who have historically claimed to be 'confessional' Anglicans committed to the formulae of the Church of England, apparently forget these principles when it comes to those deft and significant changes introduced into Cranmer's rite in 1662 to restore both the terminology and the logic of Consecration.
We know, moreover, that the 1960s Roman Catholic Reformers were simplistic and orientalising in their insistence upon creating, in their new Eucharistic Prayers, epicleses of the Holy Spirit. But the ethos of the Western liturgy reminds us that the Holy Spirit should be invoked: by the celebrant and his ministers. The Praeparatio ad Missam contains no fewer than seven collects invoking the Holy Spirit. One of them, which featured also in the Sarum Rite among the vesting Prayers at the Foot of the Altar, is the collect Deus cui omne cor patet [Sarumists in the Adur Valley will probably remind us that it was preceded by the entire Veni Creator; a lovely way of recalling one's ordination before offering the Holy Sacrifice], which survived into Dr Cranmer's rite as Almighty God, unto whom all hearts be open ...
That's our tradition.
*The assumption is that regarding a dozen words as consecratory is mechanistic if not superstitious; seeing 938 words as consecratory is enlightened and unproblematic.