Can someone tell me how a foreign lawyer might go about applying for a traineeship in London/UK? Is it possible to do an LLM part-time and work as a trainee?

I have talked with the people at the Law Society, and it seems because I have a year of experience in a common law jurisdiction, I might only need one year of training rather than two. Any advice on how to apply for a traineeship as a one year contract?

Are the traineeships usually paid or unpaid?