My best advice for prospective grad students is twofold: first, find your favorite authors. Where do they teach? Second, and more importantly if you plan to pursue an academic career, mine the bibliographies of books you're interested. Where do those authors teach?

If you have any undergrad experience in history, it might be worth an email to a friendly former professor. If anyone knows the real deal, it will be someone working in the field. Best of luck!

I know it sounds like the best programs in medieval England should be in England, but that's not actually the case. The academy is much less localized than you would think. There are extraordinarily strong medieval programs at Notre Dame, Saint Louis, UCLA, and many, many others. Doing your MA in England isn't necessarily the wrong choice, but it's a very different style of schooling which doesn't always suit American students very well. As others have said, look for scholars who write about the things you want to read about. But don't limit it to geographic scope, look for authors who take similar methodological approaches as well. Are you interested in feudalism? That's sort of unpopular at the moment, so that will narrow your choices. Are you interested in cultural history? That's another thing to take into account.

If you are set on going to England, Leeds is quite well-known. It has a large medieval congress which gathers in the summer, so there's a pretty good flow of scholars through the area. But don't rule out the quite excellent universities here in the States!

Edit: I just noticed you specified military history -- St. Louis University does have an edge there.

Brit here! I completely agree with what's been said above, don't at all feel as though you have to come to the UK to study this period, there are some amazing courses nearer to home and the academic medieval community is vastly spread out and has many connections all over the globe. Definitely talk to a scholar you respect and see what they have to say on the matter.

However, if you do want to come to Britain, you might want to look at East Anglia, Kent, York and UCL as well as the ones you've already mentioned. They all have very strong medieval departments and the benefits of studying in especially Kent or York is that you are living right amidst the rich medieval heritage - medieval archives and buildings are right there on your doorstep. Take a look at at their websites to see the programmes they offer, they're usually fairly detailed so you can see which course suits your interests best. Hope that helps.

York, Oxbridge, and Toronto constitute the world's leading medieval schools. You will need to attain what equates to a 2:1 equivalency here under the English system to get into York and the other 'top' MA courses (which include UCL, KCL, Leeds, Kings, etc.). A First is likely required to attend Oxford and Cambridge.

Unfortunately the family you want to study (Tudors) is one of the most awkward in terms of periodization. They fall into both the late medieval and Early Modern periods; the Tudor and the sixteenth-century is somewhat of a period in its own right (some simply call this the Renaissance/Reformation period). That said, if you want to study literature, politics, and martial culture before the introduction gunpowder (by that I assume you mean infantrymen with gunpowder) then Birkbeck would be a terrible choice (as it has no scholars who operate in that field, as far as I am aware). In fact the majority of the London universities (UCL, KCL, Queen Marys, Royal Holloway) tend to be focused on the period prior to c.1300. I can't speak for Bristol or Leeds but, as others have said, you need to do your research carefully into their departments and what modules will be offered on the MA. If you were to open up your study to the fifteenth-century in general (the Tudors only succeed to the throne in 1485) then I would highly recommend the University of York. You will however, be forced to step outside of your comfort zone (and preferable research period) if you are not taking the language and paeleographical courses.

If you're certain you are not interested in academia as a career then you won't need to focus as much on learning Latin (although French will be essential). I'm sure you're aware that these two (and not English) were still the primary diplomatic languages of the fifteenth- and sixteenth-centuries. There is nothing stopping an English graduate from moving into medieval studies (which tend to be interdisciplinary anyway). However, you will require more than a passing interest in the subject to get anything meaningful out of the course. What work have you read on the Tudors (from both a literary and historical point)? What do you understand about how Tudor society operated? What can you say about the economy or legal customs? What do you know about religion? What do you understand of historiography or the social sciences?

Being ignorant of one or two of these areas is fine but if you struggle to answer any of them then you might want to reconsider applying for MA courses until you are ready. An MA is a substantial investment of both money and mind - I would not recommend jumping into one without the proper preparation.