i am loooking to buy a tree for my mother's birthday. She lives in a town house and has a small walled stone garden so it would have to live in a pot. I would appreciate any suggestions as to a good tree to buy that will meet these criteria please.

Prunus comes to mind. When is her birthday?.
We could tell you which will flower at that time.

When is her birthday, Jeremy? Were you thinking of a flowering tree or one with attractive foliage?

If the former, how about a Camellia? It would need a large pot and ericaceous compost. They are evergreen, but when in flower, absolutely gorgeous. If the latter, and the area is not too hot, an Acer might be a possibility. They don't like direct sun, though.

There are lots of possibilities, depending on what sized tree /shrub you had in mind.

SNAP again, Docbob. Were you thinking about the small weeping Prunus cultivars?

If it's a sunny sheltered spot, a bay tree would do well with minimal maintenance

As Barbara says there are loads of possibilities.
Does she have a favourite colour? or flower?.
The Prunus I had in mind was Kiku-shidare-zakura, a weeping ornamental cherry, or Prunus Amanagowa a column cherry, we bought one of those for our daughter and her husband for their wedding Anniversary and it flowers beautifully every year right in time for the day in April. We do need to know the date you need it though.
As Barbara says you will need a large pot or even half barrel to give whichever tree you choose a good root run and to stop it drying out or blowing over.

If we are just throwing ideas in for Jeremy to look at, how about Salix japonica? Japanese willow. No flowers but beautiful foliage.

If in the south or west how about an Olive

Or a eucalyptus just about anywhere.

One of the many Japanese acers maybe ; elegant habit and superb leaf colour on many