What might this be?

If next door put up a fence and according to the deeds it is their fence they can tell you to remove anything you attach to the fence.

 

That's unlikely seeing as their fence posts are in our garden. We're on a hill so they'd have had a job erecting a fence without our cooperation.
If the whatever it is became an issue,I'd remove it but, despite being Londoners were quite neighbour!y

 

identify.plantnet.org says Muscadine Grape, with a 98% confidence.

 

@Escarpment Well that sounds confident! I'll look it up. I've been thinking. There's a humongous grape vine swallowing a man Wendy house a few gardens down. Maybe that's where the seed came from. Too far away for me to see if they ever get any grapes
Edit:
Google reckons they're not particularly appetising. Oh well.