I would suggest that if you want to stay in London, put Scotland as your first choice and you might just get London.
It might work, it might not...
I don't think NATS sets out to screw anyone, but you will be sent where you are needed. Your opinion will be asked but it really matters not. If ATCOs are needed in Scotland, you'll be in Scotland, if they're needed near London, you'll be in London. Personally I don't think we should ask for preferences since it sets a false expectation.
I know people who've been shafted, and those who've got very lucky.