No. You were paying for the pensions then. There's no national pension pot.
It's the success of the welfare state. Pensions calculated on life expectancy, but taking old people out of poverty means they live longer, until there are more retired people than workers to pay the pension. Then young people can't afford (or don't want) children and, without immigration, population declines and there are even fewer workers to pay your pension.
Likewise, why is the NHS in trouble? Because people live so long. Why are people living longer? Because of the NHS. The