Distinctions here could be useful.
First of all, it is not correct to see any substantive connection between the Ordinary Form of the Roman Rite and the Anglican service.
The OF is a reform of the Tridentine Mass along traditional lines, and it restores the pre-medieval Mass (in many respects the Mass of St. Gregory the Great) while maintaining certain medieval additions that the Church deemed useful. There may be superficial resemblances between Holy Mass in the OF of the Roman Rite and Anglican services (often more in terms of the style of celebration than official texts), but these are not due to cross-pollination in any major way. This is a historically demonstrable fact. As
one link in the second post in the thread discusses, worship service structures in early Anglicanism were major ruptures with Catholic liturgy; Lutheranism was no exception: "Lutheran public worship is based on the service-book which Luther published in 1523 and 1526. He retained the first part of the Mass, but abolished the Offertory, Canon, and all the forms of sacrifice (
Old Catholic Encyclopedia).
The "formula missae" and its derivatives that were composed by Martin Luther were not the Mass of the Holy Fathers, however many similarities there may have been. At most, they represent an imitation of the Mass of the Catechumens and a "communion" service. The drastic difference is seen especially in Luther's complete removal of the Roman Canon. Again,
only recently has there been a major resurgence of "Catholicizing" the Protestant service books; mostly out of shared interest in Patristic liturgy.
Thus, while the Anglican and Lutheran services are
based on the medieval Mass structures, they are significantly different enough to be seen as veritable breaks from the Roman liturgical tradition. Certain heretical beliefs undergirded the "reforms" that resulted in the Anglican and Lutheran service books, and these drastically altered the Apostolic tradition of Liturgy in the West. The Anglican and Lutheran services may have become more and more similar to the OF – but there is no hard evidence that it works the other way around. As one priest I knew once said: "smells and bells do not a Catholic liturgy make." No matter how similar the imitations of Anglican or Lutheran service books come to the Roman Mass (including wholesale adoption of Catholic liturgies), there will never be true equality without the restoration of full communion, the acceptance of Catholic Orthodoxy, and the reestablishment of Apostolic Succession in these Protestant communities. The closest a Protestant service can be to the Catholic liturgy is probably the Anglican Use; it's certainly the best example we have to look at.
All this is not, of course, to bash Anglicans or Lutherans; it is simply to note the significant distinctions between Sacred Liturgy in the Catholic Church and the worship services of the former. There is a lot that Anglicans, Lutherans, and Catholics (at least nowadays) share in
beliefs about the Holy Eucharist...but that does not mean that the liturgies of the two former were organic developments from the Roman Rite or legitimate expressions of authentic Occidental liturgy. That is simply not the case.