I am an UK national with a 6 month visa to mainland China.

Hey, I think six months means that your visa is valid for six months. It doesn't mean that your each duration in mainland China is six months. Please check if you hold single, double or multiple entries you have. By the way, UK citizens enjoy free access to HK. They can stay as long as 180 days in HK just with their valid passports if they transit or visit HK.