English Ivy is an extremely invasive plant. The climbing and vining perennial will find any crack as a foothold to reach great heights. According to the University of Washington's Botanic Gardens, perhaps the best method for eradication is a mechanical one. The waxy leaves of the English Ivy will repel any chemical treatment, rendering it useless for small areas. In fact the over spray from any herbicide application may cause more harm to wildlife than damage to the Ivy plant itself.
Cut all climbing vines at ground level with the pruning shears.
Pull as many of the cut vines from all tree trunks and fence posts as possible. Remove as many of the vines as you can. Ensure any vines that remain are cut at ground level.
Remove all ground ivy by using the hand mattock. Dig the ground and pull the roots from the soil. Missing one or two root structures will be satisfactory as removing the majority of the roots will begin to eradicate the ivy.
Cover the root area with a thick layer of coarse woodchip mulch. Check the area twice a year. Remove any new growth of the English ivy that protrudes from the mulch.
Consult your local agricultural extension service for their recommendations on specific herbicides if the mechanical methods prove futile.