No need to @ me!
My understanding is that the proportion of international students at Oxbridge is growing. I am NOT saying that is a bad thing. Numbers of international applicants are growing in the US and almost certainly in other education "markets": Canada, Australia, Ireland.
There are more people in places like Russia, China and the Gulf able to afford overseas education, and a greater number of overseas students who will have been educated in either UK boarding schools or in international schools (that huge expansion into Asia and the middle east by brand names such as Harrow, Dulwich and Westminster.)
Many of these students will be focusing on Maths, Science, Engineering, Law, Economics and Medicine. Even by the law of averages a proportion of them will be talented enough to displace British applicants. This is not necessarily a bad thing if Oxford and Cambridge want to retain their world rankings. LSE's student body, for example only has about 25% British students, and no one suggests this is a negative.
I am not sure that the odds are stacked against international students. Its really hard to get an Oxbridge place...end of. Or a place at Imperial, LSE etc - just look at recent Durham threads.
There will be different patterns, and the question of who gets "squeezed out" may depend on what subjects target students will be aiming for, and this in turn may depend on cultural attitudes in the communities they come from. If humanities, there will be a higher percentage of UK students applying, from all sorts of schools and backgrounds. If sciences, the impact might be on international students as well.