Cut it off at the roots and remove all the ivy from the wall. Dig out roots or drill holes and fill with SBK to kill them off.

It's hard work as Moon grower says, but once you've cut the roots the ivy above on the wall will wither and be easier to pull off once it's died. Keep the base of the wall clear by destroying any regrowth of ivy each year as it soon grows back. If I'm able to upload the photo, you can see the problem we had when we arrived here, but we got rid of it with just secateurs, loppers and pruning saw.
(Couldn't seem to get photo to upload as part of the answer, so I've put it on my homepage at GoY)

or you could spray it with roundup anytime now when the plant is growing well.

Sorry Kev roundup will not do it for ivy - you really need to cut off at base and wait for dieback to remove.

oops sorry