It doesn't seem uncommon for people to move to London for career progression. However, despite 8.1 million people being from Greater London there don't seem to be a significant number of people who move in the opposite direction.
It's certainly true that the flow of people is unbalanced - more coming into London than leaving - and that this is largely due to the way that that UK's economy is so ridiculously London-centric. I suspect that the lack of flow out of London (other than leaving for university & not coming back) is in part that at the same time as doing some career progression, people are also doing some family-making and root-planting, and so you get some "well, i don't need to be in London for work any more, but I'm settled here now" effects.
I've no objection to trying to fix this London-centricness by having large employers move elsewhere in the country, but it does annoy me when people speak as if there's no good reason for anyone to object to being expected to move across the country for their work.
(FWIW, I grew up in London, left for university, and came back for work. I'm not sure I would have the last bit of that if I hadn't had the options of a cheap place to live courtesy of my parents, though. There are many things I love about living here, as well as the things that make it feel like an overcrowded, overpriced, & overly-smelly hell-hole.)
