I have heard that bicycles are not allowed in some parks in London, so I thought that maybe in Glasgow the council has the same rule.
Are they forbidden in Glasgow? Does it depend on the park?
No policeman is going to arrest you for riding in a park. I'd be surprised if you can't ride in all the parks in Glasgow (or almost any other city in the UK) for that matter.
Give pedestrians the right of way and be considerate and you'll be fine.
Yes, riding a bicycle in the parks of Glasgow is allowed.
Now even more so that there are new bicycle rental schemes in place, right at the entrance of parks.