I'm afraid, @Adam-and-Krishna0, @Mike-And-Jane0 sum it up pretty well, in fact you'll probably get better odds on seeing a rainbow unicorn in Tesco, being ridden by Elvis.
London councils are vehemently against STRs of this sort (housing crisis, yada yada) and have made it nigh on impossible to jump though the many hoops to gain Change of Use permission (which is what it is). It'll start with the horror that is trying to get through to somebody in the planning dept (if your council actually answer their phones..."due to Covid") who knows what you're talking about, less so what they need to do to start the machine whirring.
I've had friends who've thought they've made some progress, only to throw in the towel because of the treacle-like bureaucracy. Oh, and of course, your neighbours are going to get a say in it too after being given the question loaded in such a way that they'd be bonkers to let it pass.
Of course, there's alway the exception (and, dare I say it, the helpful planning dept employee), and you may just be able to pull this particular ultra-white rabbit from the hat.
If you do get permission, remember to buy a lottery ticket that day.
In all seriousness, good luck - and please do come back and tell us (hopefully good) news of your endeavours.
