I’ll clear up a couple of comments in your post.
You say that you’ve just completed the TEFL; many people new to EFL say this but to an employer is doesn’t carry much meaning. Basically, TEFL is a subject just as history and maths are. We don’t say “I’ve just completed my geography”. You need to say what you have done in TEFL: is it a certificate in TEFL? A six-week online course in TEFL? Etc. You should have this somewhere in your course description or somewhere on the certificate if you received one. I suggest you make this clear on CVs and when speaking to potential employers.
As for British Council requirements, not all schools are associated with the BC. Some schools request visits from the BC in order to be mentioned in the BC recommended lists. Some schools don’t request this and some don’t meet the criteria during the visit. This means that there are schools who don’t impose the requirements that you mention. Obviously, the standard of teaching will not be the same in these schools as in a British Council recognised teaching centre.
If you are looking for work in the UK, you could start by looking at schools that are not on the BC list. I don’t know how you’ll find them. You could do a search on internet for language schools in your area and then check out the website of each school to see if they are BC recognised.
A final word about looking for EFL work in the UK: it is a very competitive market. There are a lot of students during the summer months but schools can be very quiet the rest of the year. While you might find a job in the summer, not all schools have vacancies the rest of the year. There will be a lot of competition for the few jobs that do exist; teachers who have taught abroad for years sometimes wish to settle in the UK and look for teaching work; remember, you’ll be competing with those people for a year-round job.