Pokeweed (Phytolacca americana)

its a perennial...

and can generate horseradish sized roots... which will be hard to kill ...

the poisonous deep purple berries are an attractant to kids who like to stick things in their mouths...

use the G W search for thousands of posts about such ...

kill it now.. or you will spend the next decade pulling seedlings out of your garden ...

and try to dig up the root.. all of it.. or drip round up on the cut stalk ...

ken

It can't spawn seedlings unless allowed to form and drop seeds.

That looks like a good spot for killing with boiling water, after cutting at ground level, if you don't feel like digging. The Aegopodium and Vinca will very quickly cover the tiny dead spot this would make in their quest to cover the whole earth.

Thanks so much for all your quick responses! I went out there and dug all those up right away!

At the weekend our anniversary rolled around again and we went out to a very expensive restaurant in a country house hotel. In their beautiful herbaceous borders were several Poke Weeds. A statuesque accent plant in a climate where it doesn't spread.