No, Barts and Warwick use MSAT too. (
http://www.acer.edu.au/tests/university/msat/intro.html ) I don't know if they have A level requirements.
So you mean you did AS levels but not A levels? I have never heard of anyone doing that before. Crazy!
To answer your question, no, there are no 5 year programs in London which don't require at least some science A levels. Even the access course at Kings has a requirement that you have A2s including Chemistry. I know the GPEP at Kings doesnt have A level requirements but really you should probably be aware that almost everyone who applies has very good A levels, in fact most people have a string of postgraduate qualifications!
Presumably you aren't planning where to apply in 4 days time (?!) so in that case you have plenty of time to sit A levels as evening classes etc. Without A level Chemistry you are going to be seriously held back, I think. You could always try calling the places you are interested in applying and seeing if they'll consider your application, but usually they will only waive the A level requirements if you have Chemistry (/something with Chemistry content) at degree level.
