Plums flower early..before cherry and apple. Pears also flower early ...but yours is not a pear. So by a process of elimination it is very probably a plum/bullace/greengage. Maybe others can be more helpful.
I don't think you'll be able to tell whether it's damson or plum until you have some fruit. Damsons and plums are closely related (along with gages and bullaces), varieties/cultivars of Prunus
domestica, so the flowers are similar. Size of the tree
isn't a good indicator because it depends on the rootstock (if it's a
grafted tree).
Doncaster, South Yorkshire. Soil type: sandy, well-drained
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Pears also flower early ...but yours is not a pear.
So by a process of elimination it is very probably a plum/bullace/greengage.
Maybe others can be more helpful.