What "UK's complex history with Tibet"? We've had virtually nothing to do with the place, it was never part of the Empire, our only involvement with it was demarcating the border of India and Tibet. Most people in the UK will not have enough knowledge of Tibet to have a meaningful opinion on the matter.
Most people would never heard of Tibet the UK does not a complex history with Tibet
I largely don't care. There are so many other political issues that are far closer to home and actually have an impact upon my life, so I tend to devote very little thought to goings on in Tibet.
Most people in general probably wouldn't know much about the Tibet issue but those that do know and the conversations I have had would suggest that most people believe that China's claims are completely illegitimate.
I met many Tibetans in India and they are lovely people but historically there was no actual country
known as Tibet. It was always accepted by the Tibetan aristocracy that they were an outpost of
China.