Which 'average' people in the UK are you talking about?
The vast majority of the people I know don't think of China in those terms. And they may call China communist but what they really mean is non-democratic rather than a comment on the market. (The term 'communist' is somewhat overloaded in everyday talk.)
And I don't meet many people at all in the UK who want their nation to remain 'great'. That's a very foreign sentiment to us - patriotism doesn't sit that comfortably. They probably do want a good life for themselves and others though.
Lastly, I think you're a bit too cynical on people actually wanting democracy for China. I think a lot of people do genuinely want this for altruistic, but also selfish reasons.