Actually, it may be possible to get near £350/month, depends how many refugees you are going to be living with
I lived way up north of London when I was there 4 years ago, 3 of us had a house with a massive garden that the landlord took care of, it was great apart from the winter, when it was bloody freezing...
If you want to live close to the centre, try looking around Russell Square area, my gf lived around there for a few years. If you want action in the heart of London, you've gonna have to pay in some way...either money, or poor living conditions...
If you want a real classy neighbourhood, try West Hampstead, my cousin lived there for a bit, but I think he was paying close to £500/month
Good luck