Do British citizen need visa to transit from Shanghai Hongqiao airport to Pudong airport?

I'm a British citizen living in Japan and have a flight from Tokyo to Bangkok. This flight involves a stopover at Shanghai but the connection involves changing airport in Shanghai (from Hongqiao to Pudong and vice versa on the way back). Do I need to obtain a double-entry transit visa? Both stopovers in Shanghai are less than 24 hours. I've read up on some of the terms and conditions and UK is not one of the countries listed as visa-exempt for transiting through China (leaving the airport) and would like some confirmation. Thank you.