Hey, I was kind of in a similar position to you
I had to leave my AS sixth form due to certain circumstances and ended up at a crap college for my A2 year. So from doing 5 AS levels, I could only carry on 3 at A2 (they wouldnt let me do the others), and they were English Lang and Lit, Business Studies and General Studies(
).. so basically only one fairly respectable A-level there.
Anyway the point is, I just decided that for now I was stuck with them, and despite having even more problems that year, I worked really hard - like you are
- and came out with ABB, and I'm doing A2 History this year, and one English re-sit, so if all goes well I'll have AAAB, which is a big difference from last year!
I wouldn't dream of applying to KCL because it's far too prestigious for me, but I am applying to some reasonably good universities - something I didn't even think about doing last year. If you really want it then go for it - it will be hard work but I'm sure you could pull it off, particularly as they've mentioned your mitigating circumstances.
You're allowed a bit of a ''risky'' uni choice anyway, so go for it!
Good luck. x