Various choices, Damsons or Bullace ( Wild plums). And the answer is yes. They maybe a little tart, but very edible when ripe.

I used to pick them for my mother when i was young. The
leaves were exactly like your pictures. She made Sloe Gin
with them. For winter chest problems I think it was.
(She was fond of the old Gin & Orange too.)

Could be Buckthorn, Owd. While these are edible they do have quite a laxative effect. I found this out when I unwittingly picked them alongside sloes for gin. Fortunately I didn't like the result because I thought it tasted like cherry cough linctus so I gave it to someone. They said it was delicious but didn't say anything about the laxative effect. I didn't like to ask!

May I had a proviso not to eat anything you are not sure about.....
(Just in case anyone unused to berries reads this ......)

Damson for sure

Leaves are wrong for Buckthorn.

Ok, Owd. Just a guess anyway but I bow to your superior knowledge!:)

Damsons make fantastic jam.

Well if you take a little bite you can soon tell sloes from damsons...Pretty sure these are damsons.s you say sloes are spiny and also their leaves are smaller.