It’s not all that different – the general concept is you apply through UCAS which is like the UK common app. You are correct, it definitely closes earlier than US applications – I think like october maybe? So yeah, you’ll have to be on top of things to get your application in on time but it shouldn’t be a massive pain as long as you write your personal statement during the summer. 

Your personal statement is like a little essay that gets sent to all the unis you apply to in the UK, so it shouldn’t be specific to one uni (if you’re applying to more than one). It should be all about why you want to study your subject and why you’d be good at it (I’m assuming you know about the one subject thing at UK unis, if you don’t let me know) – this advice from the lovely Chris (@passionthatmoves) is really good re: personal statements (it’s about law but the general principles apply). 

So really all you do is fill in UCAS (which is just like the common app in terms of information, probably a bit less detail) and then pop in your personal statement and you’re good to go! Obviously at Oxbridge interviewing is really important but I don’t think that forms part of a KCL application (correct me if I’m wrong people) so you shouldn’t have to fly over for an interview. You’ll hear relatively early about whether you’re in or not, I think usually before the end of Jan.