Unfortunately its a symptom of canker, something to which stone fruit trees are prone. If the area this is oozing from is sunken, and especially if the oozing area smells, its not good news if this is on the main trunk, because treatment involves removing affected branches entirely, which you obviously cannot do. More info in the link below

PDF]Bacterial Canker - Ken Muir

Thank you Bamboo - the gummy ooze is on the main stem. I read Ken's article, and now I'm sad. The tree is at least 40 years old :-( and laden with Damsons.

I hope it's not contagious as we have 2 more Damson trees close by. The trees stood in an orchard until 1971 when the Lord of the Manor sold the plot to have houses built on it, and our house is one of them.

I can't say that the oozing stuff smells, but then again I haven't removed it because it feels sticky.

I'm going to find a specialist. Thanks again.