Most people who have savings don't keep it in banks, because you might as well keep it in a tin under your bed with the pathetic interest rates, but I know an awful lot of people don't even have any savings at all.
I'm not convinced 80% of people have less than £500 savings, but I'd say it's probably a majority rather than a minority in that position.
It also depends on what you mean by 'savings' because I could get many multiples of the amount I have in my bank from the other places I keep my money if I had to, which I regard as savings.
My bank would always show less than £500 savings because the amount which means I would transfer it elsewhere is below that.
Just looking at my bank accounts with one bank doesn't reflect what I have in savings, or take into account that I have no debts, have paid all this years council tax, paid the water company a year ahead, have credits in my gas/elec accounts etc.. which is far more than £500 worth of bills paid in advance that I wouldn't need savings to meet if I had to use them.
A bank balance is only a tiny bit of the picture you need to understand someone's financial situation.
I know there are plenty of people without a penny in savings, who are literally waiting for the next pay day or digging down the side of the sofa in the hopes of finding money so they can eat, but it's not 80% of the country.