What changes to the culture of 1950s Britain/England would be needed for a Female Archbishop of Canterbury, of the Anglican Church of that time period?
She also has as much political power and social capital and all that kind of stuff as the OTL Anglican Church...
So no "She's just a figurehead to appease the Feminists" or something like that.
In terms of cultural reception, there are certainly precedents. Widespread sexist attitudes didn't really slow down Margaret Thatcher, for example; although there was still plenty of that around in the 1950s-1970s, I think she got around it for the simple reason that, while sexism had a lot to say about how women should act at home, it didn't define whether or how women should act as government ministers, simply because the situation had almost never come up before.
Another relevant example would be the Chevalier d'Eon, widely accepted in 18th century society despite being transgendered. If trans people were frequently trying to gain positions at court, they'd have been systematically shut out, but as a one-off it was just seen as an unthreatening curiosity.
So, I could easily believe a one-off instance of a female bishop, especially if she weren't campaigning on the issue of female clergy in general. As long as you can come up with a plausible story as to how she got her foot in the door (demographic exigencies during WWII?), it's not entirely far-fetched that she could distinguish herself and end up a bishop.
There would have been legal obstacles, but I'm sure they could be overcome somehow if everyone played along. The appointment of bishops in England is subject to royal (i.e. government) approval, but that level of the establishment has notoriously always functioned as an old boys' club, not strongly constrained by legal details.
I think many of the factors that would be needed for this already existed. The first women were ordained in the Anglican church in the 40s. Ordaining bishops in the 50s would be faster than what actually happened, but not infeasible.
Several women have founded churches before, especially after claiming to have received visions. The most well known is Ellen White, a co-founder of Seventh Day Adventism. Others include Anna Norbäck, Christiana Emanuel, and Mary Eddy.
The Pentecostal movement started in the first decade of the twentieth century. If Pentecostalism had a much greater influence in the Church of England than it did in reality at that time, then there could've been a large Anglican community who were receptive to prophecies and visions.
If an Anglican woman claimed to have received visions and her words were widely regarded as both inspired and practically helpful (perhaps she prophesied about WW2), then she could've gained a large supporter base who might've pushed for her ordination to the bishophood. The question doesn't didn't specify whether you meant the Archbishop of Canterbury, or just any archbishop - the former would need nation-wide support, but the later could depend largely on the decisions of a single diocese, so if these Penteceostal Anglicans were clustered in one place it would be quite feasible.
An alternative approach could hinge on anti-Catholic sentiment, plus a dash of anti-Semitism.
One classic objection to women in the priesthood comes from an early exegesis of a Levitican definition, which says that priests must be physically perfect. That is, no deformities, including also certain skin diseases conceived as equivalent to leprosy. In the exegetical text, they enumerate all the minimum criteria of wholeness, including "two fully-descended testicles." Women don't have those, so no woman priests, QED.
Now if you spin this as typical Roman Catholic superstitious nonsense, based on Jewish nonsense, you could elevate a woman to the priesthood in England around the time of universal suffrage. From there, you just need a bio of a truly extraordinary woman who rose during the War and became Archbishop around the time Elizabeth was crowned.
I think the doctrinal objections would be the bottleneck. Legal or social objections might well be fudged in good old British fashion, but altering the laws of the Church of England, which are believed to be "agreeable to the Word of God", not to mention going against the deeply ingrained beliefs of many millions of people, that's a much bigger deal. The C of E is both a rule-bound and a moderately democratic organisation. Both of these factors mean it has huge inertia against change, as the complex real-world history of the ordination of women in the Anglican Communion shows (http://en.wikipedia.org/wiki/Ordination_of_women_in_the_Anglican_Communion). Incidentally, some of the most committed opposition to women priests and bishops comes from women.
However it might be possible in unusual circumstances. One might be that the archbishop is, despite being externally male, actually an intersex person. S/he had grown up assuming s/he was a normal male but discovers she is female internally after being appointed archbishop. That would not invalidate her ordination as a priest or consecration as bishop. To take a parallel from real life, the Roman Catholic church does not allow its clergy to marry, but does have some married clergy, in the form of already-married Anglican priests who converted to Catholicism and remained priests. The RC church held that it could not undo the sacrament of marriage.
Having read the Wikipedia page linked to above has made me think of a less unusual possibility. It says the first real life woman Anglican priest "was Florence Li Tim-Oi, who was ordained on January 25, 1944 by Ronald Hall, Bishop of Victoria, Hong Kong in response to the crisis among Anglican Christians in China caused by the Japanese invasion. To avoid controversy, she resigned her licence (though not her priestly orders) after the end of the war." So, you just have to kill off or incapacitate all the other bishops.
