I’m not an expert, but it appears in the UK there are 1.75m undergraduates (2.7% of a population of some 66m, 87% of which is white, per the UK Office for National Statistics) studying at 164 “higher education providers” (of which 135 are universities) in the UK (http://www.universitiesuk.ac.uk/facts-and-stats/Pages/higher-education-data.aspx).
Contrast that with the US, which has some 4,600 degree-granting higher education institutions serving some 19m undergraduates (per NCES: https://nces.ed.gov/programs/digest/d13/tables/dt13_105.20.asp), or about 5.8% of the population. College is much more of a “thing” in America.
Meanwhile, apparently about 20% of Oxford undergraduates are non-UK (https://www.ox.ac.uk/about/facts-and-figures/full-version-facts-and-figures?wssl=1), but, from what I can tell, about 80% are white (https://public.tableau.com/views/UniversityofOxford-StudentStatistics/EqualityData?%3Aembed=y&%3Adisplay_count=yes&%3AshowTabs=y&%3AshowVizHome=no#3). Cambridge undergraduates appear to be 21% international and 74% white (https://www.equality.admin.cam.ac.uk/files/information_report_2015-16_draft_-_final.pdf).
Contrast this with, say, Harvard, where the latest incoming class is somewhat less international (12.4%) but majority nonwhite (https://college.harvard.edu/admissions/admissions-statistics).
I think the UK has a more international orientation but is a much whiter country than the US, and the demographics of leading universities in both countries reflect that.