Not sure you can remove it all without some loss of lawn? This will regrow if you do not remove or kill it all. Dont use weed killer it will get into everything. You could try stump killer if you apply it in the first 48 hours after cutting them down but is that practicle for hedge roots? How about hiring a stump grinder? Make sure you own the hedge if its a shared boundary?

There is a product that will work - you need to get at the major root stump, plus any other larger, woody roots - please read my blog on Tree Stump treatments - click on my avatar, select blogs and its one of 9. It's only short, but tells you exactly what to do (saves me having to repeat myself!).

Mr MB successfully dealt with the roots of our privet hedge without removing - read Bamboos blog and all will be revealed!

Many thanks, Bamboo, for redirecting me to your helpful blog. I only have one more question: Seeing as I live in Spain, it's possible that the products you mentioned might not be marketed under the same name. You wouldn't happen to know the composition, I suppose?

Not without going down to the car and checking the bottle! But what you need is a brushwood killer (that's what SBK is), so whatever the Spanish is for that, should do the trick.

Thanks again, Bamboo. This morning at an agricultural wholesalers I got something that's supposed to do the trick, but like you, I've gone and left it in the car! So I can't give you any more details. I will do though in the future, when we see if it works. I appreciate your effort.