LSE would be tough to get into as it is based predominantly on your UCAS Personal Statement.
UCL is also challenging, but a lot of A-Level retakes with A*/A grades at A-Level get offers every year.
KCL is able to accept retakes, but at higher grades than the original offer.
SOAS always has places in clearing, so make it one of your choices.
QMUL, is not always in clearing, but it does accept retakes in A-Level, albeit at higher grades.
RHUL, accepts retakes of A-Levels, but at higher grades than the original standard offer.
City, is always in clearing, but you can get an offer for sure.
Goldsmiths is easy to get into as long as you have A/B A-Levels.
Birbeck is able to accomodate your studying with flexible arrangements.