iirc the average stay in a care home is about 5 years. The median is less.
So using Motty's 75k that's 375k.
Lets say you need to aim for 500k. That, with its returns (20kpa) and your state pension(12k) gives you enough to live on. Then when you need long term care, you rapidly use it up.
To accumulate that 500k figure, someone starting at age 25 in 1986, would have had to invest about 10% of their salary and put it in a global equity fund. Those beat cash savings rates.
What's the chance that someone earning an average salary at 25, which is now £30 - 35k, would put 300 - 350 quid in a month, and increase it with their salary over time?
"FAT", I would suggest.
If they happened to be starting their contributions at a time when the stock market decided to go backwards and interest rates were really low, which we HAVE had, then the percentage needed goes up to 13 ish percent.
It sounds like a person would need to take out insurance on how long they're going to live. Or hand over their 500k, which a company uses to pay for your care if you live longer than average, and gains from if you don't. Like an annuity, but different.