I did medicine at Oxford and a lot of my friends went to London, so I'm relatively well positioned to comment.
The location is a huge factor - 6 years is a long time to be in one place, and the contrast between probably the most rural med school there is and London couldn't be bigger!
Although Cambridge has a reputation for being expensive, you will save a LOT of £££ by going there compared to London.
Cambridge - college system means socialising with lots of different people rather than what seems to happen at Imperial where medics form their own clique and don't talk to other people (? correct me if i'm wrong people). University (i.e. college) accommodation way more available in Cambridge. Way more participation in sports/societies in Cambridge (though if you're a high level athlete Imperial may have better facilities for you).
At Imperial you get a free iPad mini when you start clinical school (
). Might stop by the time you arrive though, can't be certain.
In the clinical years Imperial is way more logbook-governed and your attendance monitored a lot more closely (as one of the doctors on here put it who went to Cambridge and now works with Imperial students - "Imperial students have to get a sign off to wipe their own ass"), Very different compared to Cambridge where they trust you to be an adult and do what helps your learning with only some logbooks.
Both main hospitals are huge tertiary centres so will have plenty of obscure cases. Imperial might get a few more though (though does this really matter to you? You don't need to know about obscure things as a med student). Imperial will also have a more diverse patient base than Cambridge - more TB, HIV, sickle cell etc.
Traditionally London has had a very high student to patient ratio i.e. the place is crammed with students. However, Cambridge just literally doubled the size of its med school for the clinical years. I personally wonder about how they are going to fit everyone in. Open to dispute.
Feel free to ask for any further clarification, though as I clearly went to neither of these unis I may not be able to say any more.
Indeed - they were forced to!
Cambridge only had space for a certain number. Some would choose to go, then the remainder had to apply back to Cambridge in a competitive process involving interviews etc
Doesn't happen any more though as you say.