I am going to China for 12 days then to Hongkong for 4 days do I need a visa if so how much will it

Hi there! You don’t need to apply for an entry permit to HK because UK passport holders can enjoy free entry to HK for a stay of no more than 180 days.
But you need to apply for an entry permit to mainland PRC and you can apply for a tourist L type if you go there for sightseeing purpose, and it costs 151 pounds.