Hi Graham,
It's difficult to tell from photos of just the fruit, because they don't give us any information about size, or about the rest of the tree, e.g. what the leaves look like. On the other hand, with these plum-type fruit, it's very difficult to be sure in any case, because they cross with each other, so there are lots of hybrids around. Also, what's called a bullace, for example, in one part of the country may not be the same thing as a bullace in another part of the country.
So yes, it's probably one of those. Without better photos, I can't entirely rule out something more sinister, but if you're able to recognise it as "damson or bullace or something like that" then I should think it's very likely exactly that!
When it comes to deciding whether to risk eating something or not, the general rule is that if you're not confident of what it is, don't eat it. I wouldn't advise passing on responsibility for making sure things are safe to civic gardeners, especially as public parks are not usually meant to be eaten 
I learnt that if the question is, "Is it a sloe or a damson?" the answer is probably bullace.), but I can't remember how sour they were. I think they were good to eat raw. Maybe someone who knows these fruit better can shed some light on that. 