You have a PROBLEM - ivy (especially English Ivy) is one of the toughest plants to stop, especially if you do not want to get rid of the ivy entirely, but rather just restrict its spread, because the roots spread like crazy.
To totally eradicate it, there are two chemical killers that work, but will likely take several applications over the course of a year or so. Mix some Dawn inwith it before applying to help it cut through the natural oils on the leaf surfaces.
- Lilly Miller Blackberry and Brush Killer
- Dow AgroSciences Crossbow
Organophosphates like Roundup do not work very well on ivy.
If you want to keep the ivy patch but limit its lateral spread, these methods have been used with limited success:
1) dig a 1 foot deep trench and install a concrete or steel or plastic edging the full depth (not just a grass edging). Any seams or joints have to be fully overlapped and caulked and screwed (or welded) together or the roots will get through the joints. Spray the trench with one of the above killers before backfilling. Then keep the surface ivy growth cut back 3-6 inches from this border, so it cannot edge over the edging and get reestablished. Bear in mind this will slow but not stop it, as ivy roots can go 5 feet deep in good soil conditions, and can spread laterally under drives before they pop up again and start new growth.
2) set up a 6-12 inch wide "no mans land" where you want to stop it, and continually turn over and chew up this zone to 6 or more inches deep every 2 weeks or so - forever ! Do NOT let this turned up dirt mix with your garden soil,, because it has rootlets in it just waiting to take off again. Covering with plastic sheet (NOT landscape fabric) between diggings will help suppress green growth. Bear in mind this will only work if dug up FREQUENTLY, as you have to keep the roots from spreading laterally past the no-mans land into your garden.
Do NOT weedwhack it - that spreads cuttings all over - in fact, that is a great way to get it to spread, for those of you using it for brush fire protection.