I completed a CELTA at Regent Teacher Training in central London (although this was about 4 years ago). It's located near Trafalgar Square. It's a legit place, monitored by Cambridge.
I chose Regent because it allowed me to complete the course part-time (although you can also do a 4-week intensive course) and it was reasonably priced, and I only have positive comments about the place. The instructors were very helpful and informative, and they assisted me in forming connections with potential employers.
I can't compare Regent to anywhere else in London, but all of my colleagues and I were very satisfied with the course.