Cambridge is sooooo English ;) Even more English than London ^_^The "Queen's accent" there is perfect! Oxford is like that too... The "Queen's English" is often called Oxford's accent because people living there almost have it, it's difficult in Oxford to find someone who speaks with a Cockney accent ^_^
Oxford and Cambridge are said to be really posh XD More posh than any other English cities =D
If you like going hiking, authentic places and beautiful protected landscapes, the Highlands (in Scotland) is a really nice place (and a place-to-go at least once if you are staying in Great-Britain)! Highlanders are really proud of their culture and traditions ;)
And of course, you have to go to London