Just had a thought - are you sure this tree you found on Public land ---- was actually on public land and not growing in someone's hedge?
My family were farmers and we had damson trees growing in our hedges dotted around all over the place. It was a huge part of the farmers income many many (perhaps 80) years ago though not these days so I don't suppose the farmer would mind you picking them.
We used to sell them direct to Hartley's jam makers who came round in lorries and collected them, in boxes holding a score.
A score weighed 20lbs, we also sold them direct to the public at the farm gate by the lb or what ever weight was required.
Doesn't bear thinking about, but we children actually sat, on our own at the farm lane end, with a set of scales and a box of money and a trailer of damsons and sold them to passing motorists during the school holidays.
You wouldn't let your children do that now would you? 