I can't quite see the leaves well enough, but have a look at Ulmus parvifolia
Thank you for the suggestion but I don't think it's that. It's a shrub about 4feet six inches high and slow growing .I have had it about 7 years and I think it was quite well established before I inherited it. It has several stems rather than a single trunk. Produces no flowers ,fruits,catkins etc.
Sorry the leaves weren't clear enough.I have attached a crop of the image which may help
Mike's right that it's an elm but I'd go for the dwarf cultivar "Jacqueline Hillier" of Ulmus x hollandica.
I have looked up images on-line and it looks very like Ulmus x hollandica "Jaqueline Hillier" although that was described as having glossy leaves which mine are not.
I also looked up Zelkova as suggested by Mike but they looked different to mine except for one image of a Bonsai tree which looked similar.
Many thanks to both of you for solving a long term puzzle. I am both amazed and impressed by the rapid responses to my enquiry.
OK, still looks somewhat Ulmaceae, however, and probably Ulmus (there are dwarf ones), but I can't rule out Zelkova.
(Just passing comments at the moment, as seeing to other business; sorry to be brief.)
Thanks for stepping in.
You're welcome; always up for a challenge.