Certainly ask at work - at least with the People's Pension it's easily transferrable as many employers will use that 'scheme' Yes there are more than one, the state pension, and anything you pay into. I've four private schemes.
It's a bit harsh someone calling you a fool, but you need to get on a scheme of some sort as an employer has to contribute something, even a few percent is better than nothing. It's very difficult to manage on state pension alone, unless you are suddenly going to become disabled at 67 and can claim additional benefits.
Both in-laws had no private pensions and it was looking very dim for them as they came upto retirement very. Unfortunately, their son died of brain cancer, but luckily for them he had a pension scheme and they were nominated for his in-service death benefit as he didn't have a married partner or kids. That kept them going for a few years, but soon after MIL had major health issues and could then claim maximum disability benefits, as well as FIL claiming the carers allowances. This sort of saved them, but it's a bit crap living another 20 years unable to do much, being wheelchair/house bound.
My folks, on the other hand, are living comfortably in a four bed house in their 80's as my dad had a decent scheme he paid into from age 18 and he retired before he was 60.