UK passport holder cruising ending cruise in Shanghai

This is Southeast Asia 16 nights cruise provided by Princess Cruises. As I can see, your last port of call before Shanghai will be Fukuoka in Japan.

Having in mind your times and dates after your cruise is over, I can conclude that you will be eligible for 24 hour visa free transit in Shanghai and you don't need any kind of visa. Of course, it is very important for you to know that your flight out of Shanghai is not allowed to have any additional landing of any kind within mainland China and in Japan.

You will be eligible for 24 and not for 144 hour visa free transit because your scheduled transit time will be less than 24 hours long. This is not of any particular importance for you because in both cases, you will travel absolutely visa free.