This isn’t the full story at Imperial. They made a considered decision 10-15 years ago to pursue a majority international cohort. I was an RG STEM admissions tutor then and this was a hot topic amongst our informal networks.
We can only discriminate so far, with STEP being the best differentiator - and it probably is biased to the British secondary Maths curriculum. Any top degree programme in the UK could easily fill its places twice over with well qualified applicants. Home vs Overseas is not an important question for finding excellent students. The question of the very best students is imprecise, means different things to different people, changes over time, and isn’t the only basis for putting together a good cohort.
I am not sure what the obligation to cap Overseas students is, @DEI2025 If HMG were supporting UG education properly I would agree there should be a cap (everywhere)
Do you think Oxbridge bears a special burden, or would you cap enrolment at all British universities the same way?