Roundup. Use the powdered one that you mix with water and buy a sprayer off fleabay for a tenner, it works out cheaper for the amount you're going to need.
Give it a treatment then wait a week and repeat. Ask in B&Q.
Sad thing is that the roundup you can buy in shops nowadays is not a patch on what it used to be. The old stuff was deadly (to humans as well) so they had to restrict its sale.
You can still get hold of the proper stuff if you know people with licences to buy it.