Accepting multiple master's offers?

I have no directly relevant experience because I only did undergraduate history at Oxford, and did postgraduate legal studies elsewhere, but I cannot see why you should not accept offers and then only proceed as and when you obtain funding. Have you discussed with the colleges at Oxford and Cambridge which have offered you places whether they can do anything to assist you financially?
I very much hope that you can obtain funding, and enjoy your studies at whichever of the universities you go to.
The decision may be made for you by funding offers, but in case you do have a choice, I say the following.
I don't know much about York save to say that it is well regarded for history, and is an attractive 60s/70s campus university in a small, pretty, and historically interesting northern city set in beautiful countryside.
As between Oxford and Cambridge, they are equally wonderful. Oxford is the larger of the two cities, has more of city life unconnected to the university (this can be a plus or a minus, as you prefer), and has a cheaper and more frequent connection to London (a wonderful place). But there is almost nothing to choose between the two top dogs.
My natural Oxford bias prefers all brilliant historians to gravitate towards Oxford, so I hope that funding shows up, and you can go to (OK, I'm going to say it...) the Number One University on Planet Earth. [Runs way from irate Cantab friends]

Thanks for your thoughtful answer!
Yes, I've applied for need-based bursaries at the college to which I was assigned at Cambridge, and based on their reputation, I imagine they'll be able to give something, but whether that something is enough to allow me to attend or will be announced at some point in the near future is yet to be seen. My college at Oxford doesn't seem to have any sort of bursaries available, with the exception of some small studentships which don't apply to me. York has been generous to offer a scholarship to cover a bit of the tuition, but the remaining fee is still quite a bit of money.
So, we'll see. I've been in contact with people at the universities, but it seems like any news won't be released for quite some time. A bit disheartening, but I have nothing but hope.