Hello. I did the celta course a few years ago. It seems to be the course to do. I did it part time over 12 weeks (2 evenings a week and every other Saturday during the day) But you can do it full time over 4 weeks. It also involved writing 4 assignments and doing lesson preparation at home. It's quite expensive.
Since qualifying I've only chosen to use it for tutoring people at my home and for volunteering at an asylum seeker drop in. Most of the other people who were on the course (a lot were from abroad) I see from Facebook have since worked in tefl around the world. Another person who volunteered with me has worked in a language school. She has mostly filled in for holiday cover. She has mostly worked a couple of days a week. I think the pay is pretty rubbish. Also, there isn't much security in that work comes up as and when, without much notice. I remember one of my course tutors said when she was working she didn't know from month to month whether she would be re employed, although she always was.
However, I don't regret taking the course. It was really interesting. I love teaching when I do it and enjoy being my own boss. I can charge what I like. It's full of flexibility and oppotunity.
So part time is definitely realistic and there are loads of schools in London.