I don't think you can - even if you use chemicals to kill the ivy, the roots will still be there for ages. Are they very difficult to remove from where they are? I've found that even though the ivy has been cut back to ground level, it re-grows, so digging out the roots seems to be vital!

My house was entirely clad in Ivy..2 years free of the stuff and it has just appeared again.

If its only a small area you could try excluding all light from them. In a larger area you just have to keep at it. I did read somewhere that if you want to try weedkiller you could add a drop of washing up liquid to the spray to help reduce the surface tension and prevent the spray running off the leaves so easily.

Thank you all for your comments, I will try your suggestions and see how I get on.