Double or multiple entry

My wife and I fly to Hong Kong and stay one night in a hotel. We then board a cruise ship that calls in at Shanghai for one day then goes to Nagasaki and Busan before finishing in Beijing. We then depart the cruise ship and join an 8 day tour of China, spending 4 days in Beijing, 2 days in Xi'an and two days in Chengdu. We then fly back from Chengdu to the UK. Will we need a double entry or a multiple entry visa for this holiday?