Unfortunately, new EU regs mean we can't really get effective weedkillers these days, they are all diluted for us to be "safe", so are about as much use as a mop on the Titanic. Cut the ivy at the base, or as close to the root as you can, and drag it off the wall/ concrete/whatever, it will die, but it is aconstant job, you need to keep on top of it. Glysophate NEAT is the best if you can get hold of it for other weeds, don't waste money on the ready-mixed stuff. Digging weeds out the hard way is the only sure method I konw. I don't know where you live, but if you are near to a Nursery or a farm, it may be worth approaching them to spray your troublesome weeds with their professional stuff, as it is way stronger than we can buy and they will have a licence to use it. The only other method I know is to cut down as far as you can and get one of those gas cannister weed burners to burn the root down as far down as you can get. I have a garden that thinks it's been a field for 40 years, so I do sympathise!