Also sorry to hear about the heartache. I think most of us on this board have survived a few or more!
I would check out sites for flatmates...there are a few. Here's an example:
http://www.moveflat.co.uk/My/West_Hampstead/ You can plug in almost any town in London and there will be listings.
I would also look at craigslist and loot.com, and easyroommate (UK version)
London is very expensive even if you are sharing (which I am) and it all depends on where you want to live. In northwest London within Zone 1-3, you can expect to pay around £500+/month plus other expenses depending on how many people you are willing to share with. You'll need to have at the least first month's rent, and a six week deposit (most places will list by the week...a month's rent is equal to 4.3x the weekly rent). They may also want a reference. So...you'll have to have quite a LOT of money saved, not only for your first outlay of rent but also other expenses (travel, food, ect).
Best of luck to you.