United Kingdom 
I have had this plumb tree for 7 years last year the same problem happened and this year it's the same. Around late March early April it flowers, the whole tree blossoms. Come mid May and small green fruits start to appear as shown in photo 1 they then grow a bit and then shrivel up as seen in photo 1 and 2 I'm at a loss!! Please help!!
21 May, 2015
Looks like Pocket Plum, caused by a fungal infection. There isn't really any treatment, but RHS advice is to remove any affected fruit promptly, preferably before they turn white. Doing this can mean you still get some healthy fruit. Its believed this fungus overwinters on twigs on the tree - the RHS has a page on this, so Google Pocket Plum and select the RHS entry.
21 May, 2015