It appears to be a Chaenomeles, or else a Quince....the fruit look very similar, as they're the same family. Chaenomeles is an ornamental plant, normally grown for the flowers, while a Quince is grown for the fruit...people make jams and jellies from them.

Does rather look like that. The differences between Cydonia(Quince) and Chaenomeles are slight. The fruit is essentially the same and from either can be eaten.

The thickness of the twigs makes quince more likely--Chaenomeles twigs are very thin, and often spiny.

It also looks as though someone has gone to the trouble of tying in the growth very carefully against that wall....

Looks like an informal espalier. Something I hear is often done with quince, but rarely with Chaenomeles.

We have a fair number of Chaenomeles and 4 of them are carefully tied in to a trellis like that, otherwise they flop all over the border beneath. I know of at least one other garden where they are treated the same and one National Trust property where they are grown as wall plants. I don't think it is that uncommon. Never come across any versions of it with Cydonia which is more often than not grown as a free standing tree.
Also there are no 'thorns' on any of our Chaenomeles and the branches are at least as thick, and in some cases thicker than the ones on our free standing Cydonia tree.

Not so rare as I thought, then! I wasn't talking about the branches, but the new twigs--this years growth. On Cydonia, they are about as thick as an apple tree's twigs, but on Chaenomeles they are about as thick as a pencil lead, sometimes thinner.