Let's suppose that you live in York. You have a nice house and garden worth a million pounds. Your cleaner lives in a smaller house worth a hundred thousand pounds. Lord Arndale has a mansion worth ten million pounds.
Let's suppose that York City Council has a budget of a billion pounds, and it is all gathered from local residents. At the moment, you pay a council tax of a thousand pounds a year, and your cleaner pays a council tax of five hundred pounds a year. Lord Arndale also pays a thousand pounds a year (Council Tax Top Band for York).
So your house is worth ten times as much, but you only pay twice as much as your cleaner. Lord Arndales house is worth ten times as much as yours, but he pays the same.
Tomorrow, York will still have a budget of a billion pounds, and a billion pounds a year is what they will still collect.
They will divide up the LVT according to the value of the properties in it.
Lord Arndale will complain a lot. Luckily for him, he has a lot of rich and influential chums among the government.
If LVT ever comes in, the time will come (after any transitional arrangements) when he pays ten times as much as you, and you pay ten times as much as your cleaner.
It is to be expected that the price of property will change, and some people will reconsider how much of it they wish to own.
The Tory press will pretend that the amount of tax gathered under LVT will be more than the amount under Council Tax. This is not true. The amount of tax each person pays will be in proportion to the value of the land. I don't know how many multibillionaires are paying very little.