Depends on how much you want to spend. Personally, I venture just outside of SE1 down to Silwood Street (off of Rotherhithe New Road) in SE16. I'm not sure of the name or precise address but there is only one tyre outlet down there - it is about three quarters of the way down on the right-hand side. I've been there a few times over the years.
You can pick up very good part worn (fitted while you wait) tyres for upwards of £8. I had three very good part worns put on my car for about £30 a few months back. No connection with this place; just a satisfied customer.
I always used JetTyres in Hercules Road, they were quick and efficient and Michelins on a taxi were quite a reasonable price.
No idea how they compare price wise on a civilian's vehicle though.
Out of curiosity, what's wrong with Kwik Fit?