Is this some sort of buttercup?

[Imicola]

The leaves don't really look like what I think of as buttercups. And if I leave it in my border, will it end up everywhere? I quite like it, but not that much!

Wood Avens, Geum urbanum. It's in the Rose family not the Buttercup family.

It looks like wood avens. A native geum. Likes shady spots. Can be quite invasive. But you could just keep it under control? Good ground cover under trees it's hard to grow stuff under!

Ahh, interesting, thanks. It's right next to some geums (which have all been flattened by the pigeon) and I initially thought it was also a geum... and it is, just a different type! I'll leave it be for now but keep an eye to prevent it taking over.

Yes, it will end up everywhere. The seedhead is made up of multiple seeds each with a hook, so they get carried on pet fur, clothing etc. It is tolerant of shade, so can soon dominate particularly areas under shrubs.

Its rather more attractive (to my eye) cousin Geum rivale (Water Avens), with larger apricot coloured flowers, seems a lot less inclined to spread.