Looks like your run of the mill sour cherry to me.

The greengage plum produces firm fruit with flesh and skin which remains green even when ripe. If you want the tree to produce a crop of fruit for you, maybe you should research any pruning techniques which need to be used to stablize your prune tree and to help it produce its best yield of fruit each year. Also, prune the trees near it in a manner which will provide your prune tree with the right amounts of light that it needs to successfully produce that good crop of fruit. It certainly is good that pests do not bother the tree and fruit.

The leaves sort of look like ash to me. I'm not and expert at identifying them but it looks sort of like it. I can't tell from the picture if it has opposite branching. If the branches are not perfectly opposite one another on the trunk then I am mistaken and it is not ash. I'm also not so sure ash would grow where you are but it's something you can look into.

Birch, possibly river birch, Betula nigra (from what I can see of the bark).