<p>Keep in mind that getting the money to go to Oxbridge is vastly harder than actually getting in, for non-EU. people. In the math departments, there are no paid TA or RA positions; I think that this is true for every department, though I'm not sure. So, for instance, if you want to go to Cambridge for math, you would have to get either a scholarship from a college (maybe one or two for the more math-y colleges, like Trinity, are given out each year); get a Marshall scholarship (pretty difficult, but possibly doable); get a Gates Cambridge scholarship (~Marshall, in terms of difficulty); get an NSF fellowship (not so difficult). I don't know if this generalizes to all departments, but my impression is that getting funding is the hardest part of the game.</p>
<p>(Oh, and also, at least in the math departments, PhD students aren't allowed to work.)</p>