Hi Anne, have you checked under the leaves, didn't see them on my tree till a turned over a leaf

The leaf damage is Black Spot, one of the many which attack most trees. Not a lot you can do about the already damaged leaves and these days there does not seem to be a spray either. Rose Clear might work, but it is not designed for edible crops. I used to use Copper sulphate, but.............
The damage to the fruit is possible the exit wound from a Plum moth lava or wasp damage. The re is little one can do about that either at this stage. Pheromone traps from May onwards do help a little.

Thanks Taz but yes I have checked under the leaves and there is nothing to see. Thanks Owdboggy, at least now I have a name for the problem and can consider pheromone traps for the future. There are quite a few wasps around come to think of it and I've found that they do love plums especially when they are ripe!