Council tax is a weird, awkward compromise between the poll tax that Thatcher wanted and some kind of progressive tax on wealth. I agree that it's dysfunctional, but I fear it's politically impossible to change.
That's before you even get into the fact most properties are still banded according to 1991 valuations.
Reduce payments for everyone in the existing bands, and hike the payments dramatically for the new, higher value bands.
As with income tax, have the most wealthy paying the majority of the tax.
This is a slightly less crude version of the 'Mansion Tax' Labour and Lib Dems have previously proposed.
If you own a £5m property which is appreciating even at an extremely conservative 2% pa (£100k), you should be paying a lot more than £2k pa in tax.
Regardless, I can't see revaluation with higher bands not being net profitable even in the short term, or any reasons why revaluation shouldn't take place after quarter of a century.
Taxes on property transfers (capital gains, stamp duty, etc.) also create hysteresis in the market, which should be discouraged.
It's much easier to implement a council tax style system, with non-payment a criminal offence, and the ultimate (if extreme) threat of property confiscation quite practical to go through with.
Offshore registered properties without named beneficial owners are only a problem if you allow UK freeholds to be held by shady foreign entities and don't have an especially punitive tax regime just for them.
Council tax style systems suffer from property owners (particularly private householders) often not having disposable cashflow remotely comparable to the value of a house they might have acquired many years ago, especially pensioners and especially in London. (whilst I'm sure in practice, private sector equity share schemes wouldn't be too unhappy to lend the house-rich the cash, I can't see council taxes as aggressive as hypothtetical capital gains taxes being politically possible)
As you mention, many people will be able to borrow against the value of the property to pay the taxes.
Unfortunately it is indeed a political problem. What the UK really needs is an enormous, publicly-funded house building programme, but that would of course harm existing homeowners.
Valuation strikes me as not so hard when Zoopla and Rightmove can do it. "Last sale value + average annual percentage increase in the area" is a reasonable approximation.
It would be a bit of a nightmare building in the right exemptions to not destroy the elderly and small businesses, but I don't think it's inherently impossible. It would however attract screaming from the genuinely rich. Remember the mansion tax going nowhere when people argued that £1m houses (ie 37 times median income) were ordinary?