One of the reasons I never did the move-to-London thing after uni was that even though salaries are higher, they do not compensate for the higher living costs in the capital.
However, I think there probably are better career opportunities in London/SE, if you're willing to go down there as a new grad and put up with the hardship or have parents who can help while you're on a grad scheme salary and paying at least half your wage in rent. Grad salaries in London can, in certain specialisms (IT, engineering, finance) start at £25-28k. But in London, that doesn't actually go very far, especially when you're also paying off student loans and possibly a student overdraft as well, unless you work somewhere like where I do, that offers grads interest free grad loans and the option to buy a yearly travel pass interest free. If you happen to be from London or the SE, and are willing/able to live at home for the first couple of years, then obviously, you're much better off. I would rather have eaten my brains with a spoon than lived back with either of my parents - again, a choice I made meaning I was less well off than my friends who did that and saved money to buy their own place whilst living rent free and earning a London salary.
There's also a lot of competition for those grad schemes - it's fierce. Many of them will only take students with degrees of 2:1 or higher, and only from particular disciplines. I had a humanities/languages degree, and nobody wanted to hire me, because I wasn't considered to be skilled/experienced for the modern workplace. Hence, like many graduates, I ended up doing fairly low skilled work for the first 2-3 years after graduating, and needed to gain vocational/professional qualifications in order to progress in the workplace.
Money wasn't so much a motivation for me as getting away from the drudgery of a lot of that type of work. Being tied to a phone and at the whim of a stroppy customer or jumped up middle manager whose computer wasn't working didn't do much for my self esteem. Going to work and it feeling like groundhog day, same problems over and over again. In low paid/low skill jobs, you tend to have little autonomy, and there's not much flexiblity. As I've gone towards the managerial roles, I find that I'm treated like an adult, trusted to manage my own time and workload, and that I'm allowed to give short shrift to anyone who behaves rudely or inappropriately towards me. And incidentally, I do not allow anyone in my team to be rude to helpdesk staff, IT support staff or admins - I remember all too well what it was like being dumped on myself.