can anyone tell me the name of this?

That looks like Anemone hupensis - The Wind Flower. It's very pretty, flowers late summer with tall pink or white flowers. It's a lovely thing. Lucky you!

Agree it is Anemone, it is a shocking thug. We have been putting weedkiller on one patch, every time a leaf shows for three summers now and I noticed today that it has just begun to regrow. Pathclear on the paths kills the top growth, but it still comes back. If it is everywhere then I do not envy your job in clearing it it out. Sorry

If you don't want it, send it to me ;-)

Sid, if you come to Somerset you can dig yourself a clump from my border. It spreads and I tried to limit it to small clumps this year and also used plant supports round each clump - HAHA! It has escaped and is also coming up from where I dug it out....Very deep and tough roots. Like the flowers in the late summer though! Rebecca, you'll have to decide how much of this plant you want to keep after you've seen the flowers. Cut the stems back in late autumn and start digging out the clumps you don't want. Watch in spring for new growth and re-dig. Use plant supports ASAP - they get top-heavy and flop everywhere. Good luck!