Yes, lots of people live on a state pension and I expect to myself.
My mother did and most of the older generation of my family did.
I'm in my 60s and would have normally retired by now but the extension to retirement age means I'm still having to work. However, when I get to 66 I shall be on a state pension.
I don't own my own home, so I rent. Retirement villages for older people do a really low rent rate to tie in with the state pension. In such properties the TV license is only £7 per year and council tax is paid, and bills are a small set amount each month.
I currently lease a car but won't when I'm retired as I couldn't afford to; however, there is the free travel pass and the 'bus stops outside my home so I will be able to get to the nearest market town for shopping.
I already get free prescriptions and help with glasses etc. I have the smallest amount of savings, around £4000 which will be for top ups and 'treats'..... In my retirement I don't expect to be jetting around the world or taking endless holidays, I just expect to be able to walk in the countryside, join in events in the local village, write, do some gardening, see relatives, watch TV. My needs are very small and I don't eat extravagantly either, I shall be quite happy.
It all depends on what you expect from your pensionable years....if it's your chance to do a round-the-world cruise, eat out every week and live the high life, then no, the state pension won't cover it of course....! (But I have done those things in my younger years and don't want to do it again when I am older and retired!!)