The only good news about an English Ivy infestation is that it isn't particularly good at regrowing from root fragments. It can do so under ideal conditions, but generally if you take care to remove it via digging as much of the root as you can it will be brought under control with time. Most important is to remove any portion that is climbing as this is the part most likely to fruit and result in more plants (as well as kill off other desired vegetation). In other words you can use manual labor to get rid of it over time. If you are OK with it in some areas you may be condemning yourself to repeated removal in areas you do not want it as the fruits can be and often are spread by critters and birds. If you want it gone I recomend you get rid of all of it on your property.

Flamethrower. I just took down a wide swath of ivy between me and the neighbor off my fence from a rat condo complex nest on their side. We are in the woods. At first they were concerned their privacy would be tainted but then they saw my garden and said oh we can see your flowers. Leave it clear. Anyway, I use Ground Clear to keep the other neighbors ivy from creeping in the other side of the house. If you get it on the foliage only, the soil stays fairly clean to plant within two to three weeks later. You can detach the ivy from the fence and just treat what is on your side. Neighbors generally have the right to obliterate overgrowth from another garden that overlaps their property line if that neighbor is not going to maintain their side of the property. Though you wanna keep the peace too. We agreed to bring it all down in this case.

IME, removing English ivy is a time consuming process. If you have done a good, thorough job initially - specially as far as root removal is concerned - you should be well on your way to having an ivy-free bed in spring. However, even small rooted chunks can develop into new plants, so you will need to be diligent in continuing to remove any signs of sprouts. If you just removed the top growth without attempting to remove as much of the root system as you could possibly manage, you will continue to have problems.

I started trying to remove a 12x4foot patch of ivy about 10 months ago in the fall. I did not want to use chemicals, so I died digging it up. This spring, bed was full of tender ivy shoots. I took a week off of work and spent every day working section by section turning the soil with a shovel, then sitting in the dirt painstakingly sifting through the dirt pulling out all of the roots that I could find. The bed is currently has an ample supply of weeds, and minimal regrowth of ivy. In the fall I will probably repeat my grid eradication method. I should be able to complete it in a long weekend this time around. I agree with other posters that say this stuff should be illegal to plant/sell. It would not surprise me if I found the hand of Satan grasping a root as I try to pull it out. I have a negative physical reaction when I see this stuff for sale at the garden center. There should be a waiting period and required counselling before anyone can buy this stuff. Oh, P.S. I tried 30% vinegar /dish soap/table salt on a second, smaller patch. This killed the above ground plant in a day, but the ivy appears to have been emboldened by my effort, and returned with a vengeance. No substitute for elbow grease if you want to eradicate this stuff without using damaging chemicals.