I've recently retired, live in a low rent property and manage perfectly well on state pension so yes. If I discounted the rent amount, I'd easily be able to live on £10,000 pa including being able to afford my small car.
And it's possible to pick up just a few hours work per month for extras if you want holidays/small savings/treats, I've done it.
But as always, it depends upon your idea of retirement. You wouldn't be going on several foreign holidays per year unless you had substantial savings too....but I have lots of friends all across the country and go off to stay with them.
I don't eat out much and certainly don't have lots of takeaways etc., but do manage to treat myself to the odd theatre ticket, gardens open, county show and so forth, so certainly get out and about. National Trust is also worth it, one of the few who allow membership to be paid monthly, comes to only £8 each month and provides masses of free days out all through the year (assuming you drive).