I'd be pretty sure that's a no-no with the UK, but the risk is yours to take. I CAN tell you that you should NOT peel any China visa stickers out of the old passport, until you have received the new passport AND applied for and received a NEW CHINESE VISA in said new passport. Depending on what type/duration of visa you are trying to get, you may have to show or make copies of previous Chinese visa(s) as part of the application for the new one. Obviously, anything that had already been tampered with wouldn't be too good.

(Sidebar note--I have 2 passports full of Chinese visas and not a single one will allow itself to be pulled off its page in the slightest. Yet I've heard this phenomenon from others, so go figure. Maybe you get the visa version with the cheap Chinese glue. )