Right, here's the situation.
I did all my GCSEs a year early in Year 10 (that's what my school did) and didn't achieve great grades, BBBCCCC.
I moved to a different school for sixth form and failed my AS year. (DEU in History, Politics and Chemistry.)
I redid AS year and swapped Chemistry for RS. I achieved AAB in Politics, RS and History respectively.
I want to apply to LSE, UCL, Kings and Queen Mary to study History (as well as History and Politics at Queen Mary). Is it likely with a good personal statement and my current AS grades that I will get an offer from these unis?