Can a personal statement and good A Level grades cover bad GCSE's (UK) ?

i got average GCSE's..1A*1A 4Bs 4Cs 1D but in say that i got 4A's or 3As and a B in my current AS results and the fact that i've done a ton of outside activities demonstrating my skills etc etc...? and a personal statement that truly tremendous and unique..would that be enough to "cover" my average GCSE's...? would i be able to get into the likes of LSE, Kings College London ?