Have you been pruning it heavily every spring? Greengage, like most plums, bloom on wood 2-5 years old, and won't bloom if some twigs aren't allowed to mature.
Has anything changed as far as sun exposure? Has, say, a nearby shade tree grown large enough to shade it for more than half the day? Or a large building been built close to the south? Plums need at least half a day of sun to bloom and bear.

And if its Old Greengage, it needs a pollinator nearby - has anyone, or have you, removed any other trees in the last 5 years?

Thank you both for your help. I have only pruned it every 3 years .Nothing else has changed. Would a good mulching help. There is nothing wrong with the leaves. I don't think there are any fruit trees near by. Helen

Having re read your question, I see you say it hasn't flowered or produced any blossom at all - is it possible that its been caught by frost? Greengages flower quite early, and if a sharp frost comes along, the buds just drop off and don't come to fruition. Nonetheless, I'd be inclined to sprinkle some sulphate of potash around the base, together with a general feed such as Vitax Q4, water well and then mulch to see if it makes a difference. Do not apply mulch if the ground beneath is dry.

Thank you tugbrethil I am not sure whether I am answering in the right place. The greengage hasn't been pruned for over 3 years and there is no difference to the light of its habitat. I have a winter cherry near by which intertwines with some of but that was there the same size when i planted the greengage. I think it is a self pollinator.Theres a small Bramley on the other side which is too small to effect the light.

Is it still getting at least 6 hours of direct sun a day, Nelhelen? It sounds like it is pretty hemmed in, and too much shade could cause both moldy fruit and lack of bloom. Root competition may also be a factor, especially if the tree hasn't been growing at least a foot a year--that's an indication that the tree is fighting for it's life, underground.

Thank you for your continued help Tubrethil. I think I will have to get all the trees pruned, not an easy job as they are surrounded by uneven paving slabs, and then give them a good mulch. I need to get someone professional to do it, as they are big trees. As I have the Greengage and a winter Cherry. What time would be best to do them. The winter cherry blooms away happily as long as it is not frosted,
I realy want it to bloom as my Mother requested a useful tree in her memory.
Thanks again
Nelhelen
P.S, I don't know how much it grows every year, but it is a fair size. Not a lot I can do about the root is there

Bamboo would know The proper pruning times for the UK better than I would--I live in a desert, and we do all of our pruning in mid winter to prevent sunburn! On a more general note, trees that are pruned will present less root competition to their neighbors because they use energy that would otherwise go into root growth to recover from the pruning. It's good to get an expert, because wrong pruning could stop bearing at best, or invite disease at worst.