Around 150 people, across ALL subjects, turn down Oxford offers each year. I don't see any reason why the figures for Cambridge will be terribly different. What does this mean? You're not going to find many people doing physics at Imperial who got offers from Oxbridge. Oxford taake around 200 people a year to do physics, or around 1 in 15 of the year as a whole. Assuming physics students turn down offers as regularly as those given offers as a whole, that's around 10 people. Double it for Cambridge, and even if we make the gargantuan and utterly unfounded assumption(albeit one that weakens my point, hence justifiable) all thosee people go to imperial, that's still only 20 people doing Imperial physics having received Oxbridge offers each year. I'd hazard a guess that, unless Imperial and Oxbridge look for mutually exclusive (for the most part) qualities in applicants, most of those who go to oxford to do physics will have received offers from imperial.
If most students at uni A get an offer from uni B and very few at uni B get an offer from uni A, that suggests to me that there's quite a pronounced difference between how difficult it is to get into each one. Competitiveness is contingent upon the quality of the application pool, not just it's size relative to the amount of offers given. Those two factor's aren't necessarily correlated. Do let me know if you feel I've made any unjustifiable assumptions or invoked any kind of shoddy reasoning (there are certainly some points of my argument that could be made a bit more explicitly, but I'm slightly drunk so, pfft). I suppose I've not accounted for the possibility of there being some massive pool of applicants who go for Imperial but not for Oxford. it doesn't some terribly probable