Its not exactly quick nor easy, but nothing else will work. First cut every branch and stem arising from the base, all the way along. If you can't see the base clearly, hack it back until you can. The topgrowth can either be pulled off or left in place to die - be aware that, when you pull ivy stems off something, they stick like the devil, and will likely damage the wall if you try to remove it all, especially if the wall is old or has old pointing.

Now comes the boring bit - you need a bottle of SBK, a brushwood killer. You need to drill into or make cuts in the stems above ground (they should be cut of virtually at ground level) and treat each one with the SBK, without spilling it on the soil or anywhere else. Cover it all up if you can,doesn't matter what with.

Next year, check the area - retreat where necessary, and it may be necessary to dig down and treat the larger roots with the SBK, so buy the larger bottle, not the 125 ml size.

Yes its tempting to pull it all off straight away. But if you can bear to wait several months until its gone quite dry and dead it lifts off much more easily and causes much less damage to the wall than if you do it straight away. And the thick parts make wonderful firelighters once its dry.

Thank You, Bamboo and Steragram, I have tried almost everything. The problem that I have is, that it is growing between a shed and a wall with only a three-inch gap. I will have to move the shed. It has already ruined the rendering in the wall. I will do as you recommend. Thanks again.

Ooh dear, I'm afraid you will have to move the shed,let's hope its not on a concrete pad, because there'll be ivy roots underneath it. Its not worth putting the shed back there until you know you've dealt with the ivy thoroughly, and that you won't know for sure for a couple of years.