Are these sloes?

They look like sloes to me. We have a whole lot of these on our golf course and plenty of people make sloe gin - if you do make it then be sure to 'prick' the sloes before soaking them in the gin.
Our damsons are much bigger and much sweeter than sloes although the purple colour can be much the same.

 

If the tree has inch long spikes that skewer your hand as you pick them, they're sloes, if not, they're damsons.