Peter and Peter's Grandma,
It is one of the sallows, and I lean towards the common sallow, Salix cinerea (also called grey willow).
It does, however, hybridize with close relatives, such as Salix caprea, so one can't be completely sure.
It was probably not planted by human hand; they often spring up of their own volition from wind-blown seed.
Thanks Mike for the information, I can now let my mother know as she has been wondering about it for ages! It does look stressed as the leaves are yellowy it is growing on top of a hill on chalk.
Sallows are pretty tolerant of various soil types, though the (probable) dryness of the chalk won't help.
Whenever you see yellow leaves on a normally-green plant, see if it is primarily the older leaves that are yellowing. With evergreens in particular, the old leaves do get shed eventually and they go through a yellowing stage as part of that. Some deciduous trees, too, may shed some leaves in late summer, yellowing on their way out. I'd be concerned only if I could not ascribe the yellowing to either of those causes.
Best wishes to your Mum.
I have just spoken to my mother who is very greatfull for your help, and promises to look after it!
PS she has only recently got an ipad, but is not able to use it much yet hence my involvement.
Your Mum and her iPad - bless!
I bought my Dad an Apple Mac for word processing (don't ask which one - it was a long time ago!); he tried, but he was happiest using his old Smith typewriter. I hope your efforts with your Mum prove more successful.
Now look - she really doesn't need to promise to me to look after her own tree!
It was a sweet gesture, though.
To be honest, sallows can outgrow their position in a garden, especially if self-sown. And they are of limited virtue, especially in a small garden (though the flowers are liked by moths). So it might become necessary to prune it one way or another, or to have it out, in order to let more-worthwhile plants/shrubs/trees do well.