Wealth and income are two different things. You can be high income but low wealth - e.g. families with high outgoings living in high cost areas. You can be low income but high wealth - mortgage free, lots of assets, working part-time or retired and living off savings/investments/pensions.
Currently, the high income person is the one paying most, if not all, of the tax in the UK in the above situation.
I previously lived in Switzerland, and they have a wealth tax as well as income tax, VAT etc. It is not just for very wealthy people - e.g. if you own your home, you are already going to be liable for wealth tax. Depending on which canton and municipality you live in, the amounts and allowances (deductions) are different, but it is usually progressive, and covers your worldwide assets minus debts. The wealthier you are the more you pay. Housing is not assesed at market value but to a formula well below this level. Pension savings and certain personal possessions are excluded. The rates are from less that 0.1% to just over 1%. Some rich people move canton/municipality to minimise this tax, e.g. Nidwalden or Schwyz, but if you're not from those areas, the main attraction is tax saving tbh.
Switzerland does not have IHT (abolished some time ago), but does charge income tax on bequests if you are not direct line related - so, children no tax, parents no tax, friends and extended family taxed by degree of relatedness. Before Covid I did a back of the envelope estimation on what a 5 pro mil (0.5%) wealth tax would raise in the UK . I came up with approx £45 billion per annum. Even if generous deductions reduced that by half it's a big chunk of money - annually!
The very wealthy would not leave if it's 0.5% per annum charge that everyone with wealth is expected to pay. It's charging multiple percentat arbitrary starting points (£10 million, £20 million, £50 million) that scares off the very wealthy. Switzerland is discussing this problem now, since the Young Socialists (far left) propsed having a referendum on bringing in IHT of 50% on people with over £50 million. The vote is at the end of this month, and the Young Socialists are likely to loose (barring a major upset), since the Swiss are very pragmatic, and do not want to kill the golden goose! Imagine the wealth tax those people pay every year! A few have been spooked and left already, so let's see what happens!