This time of year plums are imported from the southern hemisphere. Places like Chile. They're picked 'backward' i.e. not ripe, and they're supposed to ripen as they travel. If they were picked ripe they'd be mush by the time they arrived. But sometimes they're picked too backward and whilst they look OK when they get here, they don't ripen properly and the sugars never develop. Asda, Tesco and Waitrose are particularly rubbish at this. Sainsbury and M&S seem to have better suppliers.
Rather than composting add them to some apples and sugar and you've got a nice Plum & Apple Jam.