It's not taxes that's the problem, you can't magically solve the problem by storing cash or gold under your bed.

If you increase demand for labour (more people getting old needing more care, more doctors) and reduce supply for labour (fewer people working), then the cost of labour will skyrocket.

Put 5 billionaires on an island and 1 carer. How much will the carer charge to care for an hour. They auction their time, and the bidding starts at £1m an hour.