Whether it raised huge amounts or not, I think that taxing wealth would introduce a sense of fairness that the UK has been lacking for a long time. Too many people work long hours for wages that have to be topped up with means-tested benefits that prevent them from being able to (eg) save for a house deposit or anything that costs over £6000, as as soon as they hit that amount of savings their benefits are clawed back. Their employers, OTOH, who are able to pay low wages because of those benefits, can spend and invest and save as much as they like, and their profits on investment are taxed at a lower rate, if at all.
The sort of education that can lift people out of low wage work costs more than many can afford, so people are trapped that way, too. Childcare is ruinously expensive, and rents on houses owned by private landlords are extortionately high, so it is very difficult for 20-35 year olds to start families, and the population as a whole continues to age.
I'm not surprised there is so much resentment of older people and of those who profit from the work of others, as so many people can't see a way out of dependency and a life of scraping by, even though they work hard. When they see others with good pensions they could draw at 60, houses that cost far less than their equivalents today and the gap between rich and poor rises year on year, resentment is to be expected. It's not about envy, before someone leaps to that conclusion - it's about basic unfairness.
I fear for democracy in the UK, as the resentments are leading to a swing to the right. People are easily persuaded that immigrants are responsible for lowering wages (and there is some truth in that, particularly at the lower-skilled end of the market), when taxing billionaires would affect very few people but bring in money that could be redistributed to make life fairer for all.