Sounds like Brown Rot, but that usually sets in more easily when other damage has been caused initially. Cut some open to see if there's a brown tunnel or horrid brown stuff inside around the central stone, you may have had a Plum Moth infestation. Thick skins may be a reaction to insufficient water at times once the fruit formed and started growing.

Bamboo. Thanks for response. You set me on a trail to investigate more. We did have a number of whitefly around and I see this can cause stress to the tree, but as the fruit is all disposed of now, I'll have to do more checking. I thought it may have been too wet as we have had an exceptional amount of rain here this summer in the NE.

Certainly if there's lots of fruits and they're not thinned out and are touching one another, damp weather may well cause brown rot.