EDIT: At a vague guess I think things were still fine in 2002-2003? Something happened then to sharply affect opinion here in the UK which was generally not negative at all, in 2002 UK opinion was 16% negative and 65% favourable. China was legitimately regarded as cool in people's minds.

It's the 2008 Summer Olympics. That was around the time when people were finally exposed to what China was actually like instead of thinking Chinese people were still riding bicycles like Chun Li's stage from SF2. You started getting press about how China's air pollution was akin to breathing in car exhaust. Add in the Great Recession where the West is no longer secure about its place in the world and Obama's pivot to Asia, and it's not difficult to see how people perception of China would deteriorate.

A lot of graphs have the same pattern: a bump in unfavorability around 2008 and a bigger bump in unfavorability around 2020.