More than likely you would need to do a conversion course before you can do an LLM. You can do an MA in law though.
Just out of interest, what do you intend to do after your degree? If you intend to become a solicitor, you won't need a law degree and you can go straight in via SQE as you are. If you intend to become a barrister, then you would only need the conversion course (PGDL).
The master's degree is appropriate should you wish to either teach in law or become a law academic.