Multi City

Hi There, I have a bit of an unusual schedule, hoping you can give some advice and I have a UK passport. I am flying from London>Shanghai>Taiwan and then on I have booked a return from Shanghai>Frankfurt>London and this is all on one ticket. I have not booked the flight from Taiwan to Shanghai yet. I will spend less than 72 hours in Shanghai both times. I think I am OK on the way there but I am unsure on the way back if I need a visa? Thanks for your help!