Thanks to everyone who has been trying to help me solve this puzzle.
I have followed up tcvarlh's comments and come up with an
image here - which has a lot of similarities - particularly the red around the eyes.
I have to admit that I wonder if this bird is some kind of cross that hasn't worked quite as well as the breeder hoped - because the white wing patterning and the nape are assymetric.
We have managed a couple more photos from the other side - although I'm not sure how much they can help.
My son took this one this afternoon:
Given what people have said so far, and the evidence of the song - which I can hear a lot of the time, even when I can't see the bird - I'm going with some kind of escaped canary. However; if it is some kind of cross breed with (say) a greenfinch - what are the laws covering captivity of such a bird (ie greenfinch) in the UK? I know that finches are commonly kept on the continent - my husband was particularly distressed by the caged goldfinches in Spanish markets.
Thanks to all.