Just apply to every job and every school, advertised or not. In places where there are lots of schools, it can be worth going round and handing over your CV in case they are stuck for a cover teacher and so will take you on short notice. And don't forget the suburban schools, e.g. Wimbledon.
And while you are waiting, get as much further training as you can, e.g. going to workshops or taking post-CELTA qualifications like the Young Learner extension or the LCCI Teaching Business.