Answer: English Ivy (Hedera helix) by nature is a spreader, climber and creeper which is why it is so useful as a ground cover. Unfortunately, apart from the use of growth retardant sprays which are usually only available to commercial applicators, I am not aware of any effective control steps besides a regular program of trimming.
To help keep it out from under or climbing on the fence, you might consider a ground barrier layer of step stones or black plastic set next to and just under the fence. This prevents it from rooting into the soil all the way to the fence and allows you a space to walk along the fence line when you trim.
In the long run, though, the trimming will take less time on an annual basis than lawn care would. (You can trim painstakingly by hand or quickly with a weed whacker, by the way.)
You might also consider an alternative non-climbing ground cover such as Vinca minor or perhaps pachysandra which is the slowest growing and easiest controlled of the three. Good luck with your project!
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