Amelanchier?

Ditto

Love Amelanchier, smothered in white flowers in the spring, followed by black berries (which will quickly be scoffed by blackbirds and pigeons), and the leaves will turn orange and red in the autumn. If your garden is in fact 'tiny', then I would consider buying a bush and pruning regularly when it reaches the required size.

WOW! Thank you all for the quick response. It is a pretty tree, although I'm not sure about attracting pigeons to scoff the berries - currently trying to discourage pigeons.
My fantasy is a flat topped tree (like in Japanese prints), white blossom with a tinge of pink and good autumn colours. It seems a big ask I know, but there seems to be so much to choose from….

How large (or small) a plant are you thinking of? There is a deciduous azalea listed on www.glendoick.com called Azalea OCCIDENTALE X ARBORESCENS. It grows three to five feet tall, white flowers with pink markings in late May/early June. I can vouch for the quality of their plants.

Check out Nandina, often used in Japanese styled gardens, which comes as a shrub but you could over time raise the canopy or cloud-prune it.
It has white blossom in panicles, followed by red berries in autumn/winter, the new foliage in spring is red, and the rest of the foliage is evergreen, which may be useful of the garden is so small that all your space is precious and every plant must earn its keep.

I really like the look of Nandina - might see if I can squeeze one in as well. I'd like an actual tree, up to 3 metres high, but one with non invasive roots. It will be in a corner between 2 garden walls, only 2.3m from the house and sharing the garden with a few shrubs, including an azalea.