The public are hypocrites when it comes to what they want and who they think should pay for it.
From this Yougov survey:
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When the public are asked what income decile they considered "rich":
We know the mean wage is about 28k, so it figures that the 8th, 9th & 10th deciles are all above average earnings. Hence why we see a big jump in the proportion of what the population on the whole things of as being rich.
However, when you ask people who are actually in those earning brackets if they consider themselves rich, you get wildly differing opinion:
Only 7% of people in the 40-50k bracket consider themselves rich, and only 10% of people earning 50k+.
This demostrates that, as you say, people want to have their cake and eat it. They want the rich to pay for it, but when asked if they consider themselves rich, they will say "no way!". The logical extension of this is that they want someone else to pay for whatever they want done.