Well, it looks superficially like an elder, and I wonder about Sambucus racemosa (which has red berries, but I can't remember if they start-off white). There are plenty of other species of Sambucus, some of which are planted in British parks and gardens. I don't think the leaves are right for a rowan, Sorbus, though some of them have white berries.
I need some more information:
Are the fruit single, like in your photo, or in bunches?
Are the leaves alternate or opposite on the stems?
Do the leaves have a foetid smell?
What is the name of the wood?
The seed pod that you can see in the photo is a paper thin double pod with a brown seed in each compartment, rather like a physalis . They are hanging off the tree with about four or five pods handing off a central stem. Pity I never saw it in flower. The leaves are opposite on the stem. It hasn't got a strong smell at all, not like the elder. It's in Slindon wood.
Oh dear - giving me a bit of a problem!
Unfortunately, I can't find a planting plan for Slindon Wood (sometimes parks and such areas os semi-natural woodland have records showing what was planted when, and what trees were on-site originally).
It is not Pterocarya, Carya, Sophora, Senna, Cedrela, Cladrastis, ...
Phellodendron: not quite (fruit goes from green to black)
Picrasma: no: leaves alternate and fruit berries
And it doesn't key-out using these:
If we don't get an answer from anybody else here, we might have to wait until you can show us a photo of the flowers.
We know most native trees but this one looks quite foreign. It is about ten foot from a footpath and there are just the two of them. Perhaps it was a bird dropping a seed say from parrot mix? Not sure what might be in some of that stuff.
I've just taken another close up of the seed inside one half of the pod and I'll attach it to this.
Definitely has hints of Colutea, as in Colutea arborescens - bladder senna.
But I can't find a species (or relative) with those leaves.
Are you sure the seed pods were attached to the same plant as the leaves?
Absolutely! I will try and go back on Tuesday and take a picture of the tree and fruit. However it is quite overgrown around it but will try and get a good shot. I appreciate your help. I've been looking at soulangeria, can't spell it! I'ts the double bladder to the seeds that is so very distinctive. Thank you, it's a bit of a puzzle!
Yes, bird seed is a possibility (to respond to yur earlier comment).
Please can give me the correct spelling of Soulangeria?
Further photos: some shots of the leaf buds might also be useful.
It will be good to know, when and assuming we get there!
Paddy - yes - brilliant - well done!
Thanks Mike it was helpful having your ideas. Helped me put the right things into the search engines. I've contacted the local National Trust so that they know it's there and don't chop it down inadvertently ! The full grown tree is very attractive. Thank you again, Paddy