It might not be as expensive as you think to live in London (or at least within commuting distance) and there's likely to be more job opportunities there than there will be local to you. However it would certainly help to have a bit of money to start you off after a move because even if you move and get a job straight away the chances are you won't get the income for a few weeks at least.
If you don't want to move to London because of friends/family where you are then I can understand that but ruling it out just because it is more expensive might not be a great plan as there are usually far more jobs and you'll often find jobs either pay more anyway and/or have London weighting to help compensate.