I can't give you a complete answer, and I have to say that I never quite worked out if this was the best, or in fact the most legally-correct thing to do, but...
I registered as a sole proprietor business many years ago, and have done a bunch of random freelance work via that registration. The full annual fee for registration is around $2500-$3000, but they often reduce that as part of their random annual tax manipulations. I only ever billed and got paid under my own name, not the business name, so I just got cheques or bank transfers paid into my personal account. On the HK tax return, I put my income down as business earnings, but I actually got two tax bills each year, one as a business and one as an individual, where I only had to pay whichever was lowest. One thing I did which I know was not legal, but was never queried, was skipping MPF - technically if you're self-employed, you're meant to sort it out yourself, but nobody seemed bothered that I didn't bother...
I also never bothered with an accountant, but I also never really made an effort to be tax-efficient. Given how low the taxes are in HK, it barely seemed worth it...
As for getting paid, depending on how flexible the company in the UK is, they could possibly pay you into a UK account, assuming you still have one, and let you transfer the money yourself - or you could look into getting paid via something like wise.com. If not, you could always just let them pay you by TT/SWIFT, which would generate some small fees. I can't really comment on that sort of thing, since I always worked for HK clients.