+1 for SW London because of easy rail routes for you and the bike from Victoria, Clapham Junction, Waterloo etc.
I don't actually know anyone in London, would it be worth looking at areas with high proportions of backpackers and suchlike to avoid the feeling of being too much of an outsider?
There's plenty of outsiders here so I wouldn't worry about it!
Relatively cheap but with low crime could be more difficult. Wandsworth has low council tax and contains Clapham Junction station for trains to Swinley, and could be a good option. Try a Gumtree flat search for Battersea?