Top 10 Uni means in the league tables. The Guardian is different to the Times which is different to the Telegraph, but broadly they're the same. You will see Oxford, Cambridge, Imperial, Warwick, Durham, Nottingham, St Andrews' in some order, along with a few others.

Where you come from doesn't matter. High tier universities don't discriminate on background any more (Though Oxford still has about 50-50 private vs public school students, that's because private schools have more money for tutoring and good teachers, bear in mind) and often have targets for working class background students.

Aiming for a University in the top 10 is a good start, there isn't much to differentiate them for Undergraduates unless you want to do a master's or doctoral degree, which is when their research specialisations start to show.