I'm desperate to move to Notting Hill Gate or Kensington from Shetland, but am on benefits - any ideas?

This might sound like a really bizzare question, but I don't know what to do. I am desperate to move to Notting Hill Gate or Kensington from the Shetland Isles to be closer to my boyfriend, but currently I am only recieving a measly �54 a week on benefits. I can't stay with my boyfriend at the moment as he only has a small flat which doesn't allow children. I would need somewhere with 2 bedrooms as I have a little boy. I have tried all the council exchange websites, but can't find a match. Does anyone have any ideas on what I can do? - It's really getting me down.