Depends how established it is.....but I would try digging it out and if it resprouts, spray it with round up brush killer....

Manual removal is really the only 100% effective method but it requires both considerable elbow grease and persistence.

English is a noxious weed in the PNW and its removal is highly encouraged. I've attached a link from a local agency that has excellent info as well as control suggestions.

ps. besides the obvious, another good reason for removing ivy is that it provides an excellent habitat for vermin......most specifically rats!

Here is a link that might be useful: English ivy control

Last fall I removed English ivy, lots of it, trying to get every sprig out of the yard. It had even crept halfway across the yard in spots. I just sat down on the ground and pulled it up, following the vines back to roots. Some of this ivy had been in place for probably 60 years. It came up easily. I think the ground was fairly soft from recent rains. I just used my hands, though I kept a trowel nearby to use if needed. Ended up with a pile in the alley about five feet high, ten feet long, and the city came out with a truck that had claws on a crane and they scooped it up. This year there has been no ivy except where it's trying to come back in from neighbors' yards. I pull up all intruders as soon as I see them.