A: depends on how desperate that TOC are for numbers where you want to live. I imagine you would be far more likely to be successful if you were applying for a London commuter TOC than trying to go the other way (ie trying to get into a small depot in a local town for example or an "intercity" style TOC). Though i'm guessing that you probably have gone to the SE to train? Said you wouldn't mind relocating and now things ermmm...Anybody been through what I am asking?
I am currently a trainee driver and enjoying, however I relocated and am finding the move away from home not as easy as I thought it would be
What is the truth with regards to
A: applying and getting in with another toc as a newly qualified
B: your TOC letting you leave
C: and would you REALLY have to pay for your training

A guy that has came over to us has had to pay 8k back to his original TOC
It's in my contract in black and white, I spoke with manager about it and said it would be dependent on circumstances or if you moved to a TOC with same parent group eg Arriva, First, Govia they maybe more lenient
I know what kind of situation your in because about a year and a half, two years ago I was in a similar postion. I moved to the SE for a trainee role and really struggled for pretty much the whole time I was down there, mostly because I was going home too much and not making a life for myself. My advice would be keep your head down and get through your training, do a year just to show you can hack it alone and you leave without burning bridges. Start applying for places back home around your year anniversary, even if it says a certain amount of time qualified just apply, it's good practice and you never know. As everyone says it all depends on what region your originally from and the demand for drivers in that area really but don't get disheartened if nothing happens for a while, you will get back. I only told close friends I was looking to move back as soon as possible, don't think management or HR knowing would be beneficial in anyway shape or form!
Just remember, your current line manager will be asked off the record on how you perform etc.