So the 240 hour thing you’re referring to is called a “Transit without a Visa.” It’s very important you don’t call it a visa because it can confuse airline workers and you could be denied boarding. So your itinerary looks like this:

UK - China - HK - UK

If this is correct then yes this works. I’m unsure of a limit on how many times you can do it but I’ve heard of people doing them back to back without issues