Hi Andrew,
I live in London and have just bought my third property here. I've been here for over 5 years now and I'm a permanent resident so I no longer have any issues with buying property. However your choices of mortgage providers are limited if you don't have permanent residency (but not impossible if you have the right broker). I would suggest that the first thing you do is to get yourself on an electoral roll.
Also, as Ruby suggested the singingpig website is one of the main ones for property over here.
If you want any more information then send me a PM.
Regards,
Rachel