Arriving in Beijing by air from UK. Spending three days there

The stay in Beijing is within the 72 hrs exemption. Arriving at 7am on the 9th of November and joining the cruise ship, diamond princess on the 12th of November. Visiting Busan, Nagasaki, shanghai(17th November for one day), Hong Kong, Ho Chi Minh, Bangkok and Singapore. Flying back from Singapore to the UK. We are UK passport holders. Am right to assume that we don't need a visa? I am also aware that the entry rules for cruise ships have been relaxed in shanghai.
Could you please enlightened me. Thank you