Mountview
Arts Ed
Guildford School of Acting (GSA)
Laines
Italia Conti
You want a high quality very selective agency.
Also depends if you only want to do MT or if you are interested in screen acting as well.
Graduating from one of those colleges means something in the sense that you should get good training and the more desirable agents are more likely to attend the showcase.
But when it comes to getting cast, nobody cares what piece of paper you had, or where you trained. It's all about being the right fit for the role. It's not even about being 'the best'. You could be the best dancer in the room but 2 inches too tall to fit with the other cast members. Or technically the best singer but you just don't look right for the role.
There are also plenty of successful MT performers who didn't go to college at all. Most of them were very successful child performers who just transitioned straight into adult work. Obviously most take classes, but they haven't spent 3 years at college.
In terms of what people do between jobs - teaching, waitressing, bar work, retail. Whatever is available and flexible.
You need to be incredibly resilient, hard-working and need to do this like you need to breathe. A huge amount of your time is sat waiting for an email with an audition, waiting to hear if you are recalled, waiting to hear if you are through to finals... and generally you only hear if you are through (so you spend your time trying to find out if others have been so that you can stop dreaming about it). MT slightly easier as they often cut in the room - literally ask 2/20 to stay behind and the rest can go.
Are you considering applying?
It's worth looking at just how few places a lot of colleges have - GSA have just 22 places on their MT course and iirc it was 4,000 applications this year.
Just to add, I speak as a parent of someone who was a West End child performer, has been training since they were 4 and is still aiming at this as a career but taking a slightly different route in order to have more options.