I'm not sure I understand what your situation is. Are you looking for work as a private EFL tutor or are you looking for employment with schools?
If you are looking for work with a school, I think your margin for negotiating a salary is fairly slim. In both cases, it's important to do your homework: check similar job ads to see what salary is mentioned, talk to other teachers to get their ideas. As for private tutoring, look at the ads of other tutors. How much do they charge? And how do you compare to them re experience and qualifications?
I'll also put your question into an open forum. I'm out of touch with the UK EFL scene and don't know what the salaries are like there now.