Getting a job in London is a matter of how much you want it. If you treat finding work like a full time job, you'll get one eventually.
An acquaintance of mine moved to London from Ireland. He spent a couple of days working on his CV, which he then printed off en masse. He left the house every day at 9am, and came back at 5pm, spending all the time in between going speculatively into businesses and giving his CV to managers. After doing this daily for almost a fortnight, he got a job in a clothes store.
This guy had no qualifications and a patchy work history, but he hustled for work and he got it. If you want a job in this climate, you need to do the same.