One of the problems that Anglicanism faces today is that no-one is quite sure what it is. Even among those of us who self-describe as orthodox or conservative; some try to make it into Catholicism with married priests; others into 'Western Orthodoxy;' a few more into the English version of Calvinism; and so on and so forth. In many respects, it is almost easier to say what Anglicanism is NOT, but I suspect that might have to do with both the 16th century need for a broadly based, national, Protestant Church, and subsequent pressures towards an inclusive orthodoxy, rather than anything inherently vague about the formularies. Certainly in the initial phase after the Marian Reaction, Elizabeth and her counsellors could not afford to exclude anyone except the diehard Papists, and the initial settlement reflected this, with the Supremacy, and the BCP being restored in 1559, but the drawing up of a confession was postponed until 1562/3, and even then it was to be 1571 before the Settlement attained the shape it was to very largely retain until modern times.
However, in order to understand where "the Settlement" came from, one needs to take a quick look at the development of the three major formularies of the English Reformation - the Articles of Religion, the Book of Common Prayer, and the Homilies. Not one of the three falls simply into a Lutheran or Reformed model, and the three of them track slightly different developmental paths, so naturally, we have to ask ourselves what was going on in each case.
I have long since come to the conclusion - after reading both Harold Browne and W H Griffith-Thomas' commentaries on the Articles - that, because of their ancestry in the Ten Articles of 1537, and the unpublished Thirteen Articles of 1539/40, the Articles of Religion are first and foremost a descendent of the Confession of Augsburg. However, whilst the Articles follow Augsburg closely in matters such as the authority of Scripture, Baptism, Predestination, Clerical Celibacy, and Church ceremonial, they can and do strike off on their own occasionally, such as in Articles 28 and 29 concerning the Eucharist, which are clearly Reformed. Much of this has to do with the fact that when the Forty-two Articles were being drafted in 1551-53, Philippism (which sought the middle ground between Luther and Calvin) was influential, as the Gneiso-Lutheran reaction had not yet set in, and the theological tide seemed to be set in favour of Geneva at least on the issue of the Lord's Supper; an area where Calvin was at his most positive and creative. When the Forty-two Articles were revisited in 1562/3, the Convocation text promoted a High Calvinist doctrine of the Eucharist within what is otherwise an Augsburg derived document. To complicate matters further, Elizabeth I, and some of her Bishops, particularly Ghest and Cheney, were not yet ready to go that far, so Article 29 was suppressed from 1563 to 1571 in order to accommodate the 'Lutheran Tendency.' Even after 1571, the Articles cut their own path between Wittenberg and Geneva being closer to the former on Baptism and Predestination, and the latter on the Lord's Supper. Later attempts by Archbishop Whitgift to move the position of the Church of England closer to that of mainstream Calvinism fell foul of, first, Queen Elizabeth I, and then after his death of James I's reluctance to accommodate the Puritans, and Charles I's Arminianism. This left the Church of England with a confession which is Lutheran in some respects and Reformed in others.
The Book of Common Prayer presents a slightly different picture. It is true to say that it draws heavily on mediaeval texts, but more often than not, there is a Lutheran model that assisted Cranmer and his assistants in perfecting the English form of the liturgy. Matins and Evensong have clear Lutheran precedents in the form of the Schleswig-Holstein order of 1535, and in germ, in Luther's comments about the usefulness of the daily Office for scholars and clergy made in the mid-1520s. The Communion Office also has a good deal of the Lutheran about it, with even the Decalogue having a precedent in the form of the Frankfurt order of 1537. Other elements, such as the thanksgiving after Communion, derive from the Nuremberg Order of the early 1530s behind which lay Luther's 'Formula Missae.' Another major influence on the 1549 and 1552 BCPs was Archbishop Herman's 'Cologne Church Order' of 1545 - which would have been pretty much hot off the press when Cranmer was working on the Order of Communion in early 1548. The Orders for Baptism and Confirmation also have unmistakeable signs of Lutheran influence. However, many of the alterations made in 1552 came at the suggestion of Peter Martyr and Martin Bucer, and have a more clearly Reformed pedigree. However, the 1559 revision tended to play up the moderate side of the settlement, with its requirement that traditional vestments and ornaments be retained, but this proved to be a passing phase as the returning exiles were in no mood to retain chasubles, and other such manifestations of traditional religion.
The Book of Homilies is a far more frustrating creation in that it has all the hallmarks of a collection of sermons that has not been edited to produce a uniform whole. Doctrinal inconsistency, within a basically Protestant framework is its hallmark. Just to give one examples. The Homily of Justification is clearly leans more to the Lutheran than the Reformed understanding of the doctrine, not that the space between them is that great. On the other hand, the homily on 'the Peril of Idolatry' seems to come from a hand that has accepted the Reformed, rather than the Lutheran understanding of that topic. This seems to be the character of the whole work, with each writer riding his hobby horses without regard to the opinions of his fellow homilists. On the whole it is a very uneven collection, which ends up having a slight predominance of Reformed over Lutheran voices. This is probably a very accurate reflection of where the intellectual life of the Church of England stood in 1548-50.
In the end one has to accept that the Church of England, and thus the churches of the Anglican tradition, if they are going to be true to the historic formularies of the Church, have to concede that the core doctrinal position of the Church is Augustinianism, and lies somewhere between confessional Lutheranism, and confessional Calvinism in its particulars. In many respects the Articles of Religion in particular lean towards the Lutheran position, but in respect to the Lord's Supper, the Articles avoid the sort of realistic understanding of the presence of Christ in the Eucharist which is characteristic of Old Lutheranism, and lean more on the 'non-realist' passages from St Augustine's writings. Modern attempts to reconstruct Anglican orthodoxy along other lines have to be understood as exercises in Revisionism, not the Revisionism of the Episcopal Liberals of the 1960s and 70s, but that of the nineteenth century 'Catholic Revival.' In one respect, the Catholic Revival was a blessing in it delivered the Church from the rather arid Pietism and Rationalism of the late 18th century, but ultimately it had little use for the Church's historic formularies hence the attempts to downgrade the Articles into an historic document, and revise the BCP to eliminate, or at least mute, its Reformed content.
Folks often lament the fact that there is not one 'Continuing Anglican Church' but the fact of the matter is that there cannot be one church when there are (at least) two theologies. The history of Churches that have a double standard, or fail to enforce their formularies - such as the Old Prussian Union, the Episcopal Church, the Church of England, ELCA, etc. - is that they end up being, at best, a group of theological parties in search of a Church, or they lapse into liberalism, and then material heresy. However, one has to set against that the fact that over much confessional rigour tends to result in churches where the overall atmosphere is 'you and I are the only true Anglicans - and I am not too sure about you!' The best chance for Anglican union is for the Articles of Religion and the Book of Common Prayer to be used as focuses of unity, accepted because they reflect the doctrine of Scripture, not on their own merits. This is usually referred to as quia subscription. This makes a range of views possible, because Scripture is open to a certain amount of interpretation, but not to the extent that one has seen in modern times in the Episcopal Church, and other liberal provinces of the Anglican Communion. The general approach to theology suggested by the English Reformation is one based upon Scripture alone, but Scripture seen through the lens of the four Latin Doctors, the Early Fathers, and the first four Ecumenical Councils. The BCP and the Articles echo this position, which Bishop Andrewes summarized in his well-known definition of Anglicanism's rule of faith as One Revelation; Two Testaments; Three Creeds; Four Councils; Five centuries. Unfortunately, even among self-proclaimed traditionalists there is a move away from that theology today.