Realistically, UCL & LSE wouldn't accept. However, if you do fantastically in your A-Levels, then you have definitely got a chance at going to respected university in London (Queen Mary, Goldsmiths, City etc.)
I'd check some entry requirements though, as for some courses they may require a C in maths, or 5 A*-C GCSEs.
In saying this, your BTECs should be sufficient as an alternative to the 5 GCSE requirements. Just study hard & you WILL be rewarded!