My suggestion is based on Henry George's idea of a land tax. George's idea had a loophole because tax would have only been paid when the land was sold or inherited, whereas nowadays the richest use trusts to stop land from being inherited.
Land Value Tax is when you tax the value of the unimproved land, so if there was a field where your block of flats is, the tax would be based on how much that field would be worth. The valuation takes into consideration all the stuff around that adds and removes value from the land, such as roads, nearby water and other utilities to connect to, schools, etc. The valuation would assume planning consent to build a building exactly like the one that's currently there.
The valuation would be done like Council Tax is done now, but on the value of the plot of land, not the land plus buildings. The value would be reviewed every now and then, meaning that the recent CityFibre rollout to my street would increase the valuation of my plot at next review because having fibre to the premises internet available to the plot makes the plot more desirable to a builder.
The purpose of this tax would ideally be to replace all taxes that punish hard work and inventiveness, such as income tax and taxes on buildings. It would incentivise landowners to do something with high-value land, like build dwellings on it. Land in urban areas tends to be more valuable than rural land, so it would encourage more urban housing to be built, putting people near their workplaces and hospitals and other useful services. It would deter the speculative land purchasing that leads to refuse-filled wastelands and derelict buildings in towns and cities, because that land would cost the owner money for every year they owned it and they wouldn't be earning from it by leaving it undeveloped. It would stop the current situation of inheritance tax bills forcing children to sell their dead parents' home, because there would be no inheritance tax any more. And it would be impossible to evade Land Value Tax because you cannot offshore land and persistent Land Value Tax defaulters would have their land confiscated by the State.
The moral reasoning is that there's a fixed amount of land and the only reason why any of us "own" a bit is because at some point in the distant past someone helped themselves to a bit and killed anyone who disagreed with them. By rights, we should all pay ground rent to everyone else on "our" bit.
George's suggestion of how to spend the money was on pensions for the old and an "adulthood launch" lump sum at 21, except that only men would get it 😕 I suggest that mostly spending it on the things we already spend taxes on would be a better alternative.
And yes, in a leasehold flat, your landlord would be paying it, and they would inevitably pass the cost to you, but you wouldn't pay Council Tax or Income Tax any more.