Inherited a fruit tree?

Samallanswim

Hi, I'm new to gardening and we've taken on an allotment. This tree which is very high is in the hedge on our plot. It's full of fruit and I'd like to pick them but I'm not sure what it is, any ideas? Thanks sam

Samallanswim

Here are some photos of the tree and fruit

fidgetbones

Plum or damson. They look a bit under ripe still.  Cut one in half and you should have a plum stone or similar.