What UK universities best resemble private schools?
You should look for the older universities & colleges. As well as Oxbridge, there is Durham, York, some of the London colleges, and one or two older Scottish universities. I went to Hatfield College, Durham University, and that college (as well as some other Durham colleges) is very traditional, and has many private school applicants. However, as state-school myself, I am not sure why you would want to do this, as very few areas of the ‘real world’ have such high-density of private-school ethos (except maybe City banking, Law firms, and parts of the Army). I would recomend you integrate with the great unwashed!