It sounds like an old ivy that started out as vaiegated, but over the years has started to revert to the original form of the plant. I've done a few jobs of removing ivy and believe me, it's a very dirty/dusty and unpleasent task. when it gets to the flowering stage, which yours has, it tends to be more of a problem and gets into every nook and cranny, even under roof tiles etc.
Several products can be found on the market that are designed to kill it- 'Growing Success ivy killer' usually retails for about �4.99 for a spray gun (spray on foliage) or you could use 'Rootout' or 'SBK brushwood killer' that can be sprayed onto the cut stems to stop it from re-growing.
Good Luck Tbird+