Part of finding out what you want to do is trial and error. If you want to do investment banking, do some investing yourself; it's never been easier to participate in a market. It might not be investment banking itself, but an individual portfolio you've created, using your mathematical knowledge would go somewhere in an interview with a financial institution, and you have London, so there's no shortage of investment banks. That career path has zero work life balance, however, if done professionally. If you want to maintain some liberty you'd need to be investing your own money your own way. This is much easier because you have much less paperwork and regulatory overhead as an individual investor than a member of an investment bank. If you don't like it, you can take a few years and make a fortune making others' fortunes and move on to something else. Having a few million affords great liberty.
I too wanted to be a professor in the States, but seeing the grim realities of the academy made me realize that I wouldn't be able to deal with the extra nonsense that goes along with it. If all I had to do was teach and research, I would dedicate my life to it. But we all know that's maybe 20% on a good day of what academics actually do. But almost all careers have this kind of extra stuff to deal with in one way or another, so don't look to avoid it just by escaping the academy. I'm in the humanities, so ymmv, but I know there's a lot of similarity.
You won't avoid these petty politics you hate outside the academy, at least not completely. It's not as if academics alone have petty fights and engage in office politics. But I do know that there is less of it outside the ivory tower. One of my mentors told me "tempers run so hot because the stakes are so low," which I found out later is called Sayre's law, and it indicates a truism about human nature; we are acutely aware of our insignificance, if only subconsciously, and fight it.
The academy fosters a tunnel-vision. It becomes impossible to imagine life outside, or that other career paths are just (and more) legitimate, or that there are other ways to make a living other than competing for an ever-diminishing piece of the grant funding. Academics tend to think in zero-sum thoughts so outside-the-box ideas, such as other careers are difficult for them to process. The institutional thinking engenders feelings of shame and fear for leaving, or even considering other options, because why would anyone want to do anything else, this is the life of the mind, the highest life!? But you can look past all that since the early-relationship glow has worn off the ivory tower.
I think you've already discerned that the academy isn't for you. You can be happy doing just about anything you find fulfillment in. If it's making million dollar trades, or laying brick it doesn't really matter. You just know its certainly not research proposals and bitter backstabbing academics who don't appreciate your contribution to the institution, yet depend on you for their status. You can work hard without an advanced degree and climb the ladder just as well. With at least a 4 year degree you'll never hit any glass ceilings anyway. I speak as an American. I know you folks across the pond have more stake in social status, so it might be slightly different over there.
But to specifically answer your other question: No one who quit a PhD ever felt bad for quitting a PhD. They usually just feel bad for not quitting sooner, or for going in the first place. They regret the lost years filled with stress and low income, and not the missed opportunity for a very, very, low chance of a tenured position.
