The problem is that there are actually a lot of people who do not earn enough to be able to put enough money aside to provide a pension large enough to live on, even with a state pension.
Look at all those on zero hours, working in the gig economy where money is uncertain week to week and pay rates around the minmum wage, all those who receive working benefits. I doubt many of those can afford to pay into a private pension and if they did, it wouldn't even be icing on the cake, more a thin (very thin) sprinkling of icing sugar.
The state pension is not the icing on the cake you must have a exceptionally generous pension yourself, to see the state pension as 'icing'. The state pension IS the cake for the vast majority of people in this country and the occupational pension is the icing.
So sad I’ve nearly finished last Jilly Cooper


