A London cabbie can only be a London cabbie on London. It would be ridiculous to say the same job doesn't exist anywhere else.
I'm not sure this is the best example, Stealth. London cabbies notoriously hold themselves apart from taxi drivers/mini cab drivers/Uber drivers, because Black Cab driver has specific qualifications and licensing, and of course you cannot BE a London cabbie outside of London. Because, obviously.
You can be a taxi driver anywhere though.
Same for lawyers - you can be a lawyer anywhere, but you can in a lot of cases only be a specific type of lawyer in a niche specialism in a handful of firms, probably in London.
Or a West End performer - there are theatres outside London but for long-run theatre or musical shows, you need to be in London or accept you will be touring permanently.
The title of the thread is "my job only exists in London" not "my career is unavailable outside London" or "my transferable skills are non-existent". Job is the singular, specific thing. It is a specific job, within a wider career.
I WFH outside London, but lived there for many many years in a career that 100% required me to live in London. Because if I hadn't lived in London I could not have got a job in my career specialism. Now I have experience I can use it, but I couldn't have got the experience without being there. Now I have moved outside London I have far fewer opportunities to do my specific job. Not none, but really vanishingly fewer.
I think people who take umbrage at this phrase somehow think London people are being myopic, and dismissing opportunities in the rest of the country. It's never that, though, it almost always is that it is genuinely harder to pursue a career you may be very committed to outside of London in a lot of industries. I wish my industry had a more regional spread.