If you are getting paid £45k in London, this would not be something you have to worry about. Sure you'd have less disposable income than Manchester, but the idea that you couldn't afford to go out is ludicrous.
No, not really. I seriously doubt there is any part of London where you couldn't rent acceptable accommodation and have plenty of money left over on £45k.
In zones 1-2 (or 3) that'll probably have to be a houseshare - but you'd still easily get a nice private room for that. The takehome of £45k is £2,797.27 /month after tax[0]. Even if you spend 50% of that on rent (inadvisable but common in London), that's still £1400 a month to play with. Which is still more than the total takehome of someone earning the London living wage[1].
I mean, you'll have to have a commute if you want a private, 1 bed flat or larger and you're working in Zone 1, but that's not exactly much of a hardship. My point is that with even the most basic level of sane budgeting, £45k is easily enough to live/work pretty much anywhere in London.
Yep, houseshare in Zone 1, en suite, ~£900pcm here. It's not somewhere to live if you want to settle/make substantial saves for deposits or cars, but you'd still have enough to enjoy yourself.
That being said, whilst London has a nice vibe, if you don't know people here it can be isolating. Been here a few months and not really found "my people" yet.