You need a proper path weedkiller, like Pathclear or Bayer's Path Weed Control. None are as effective as they promise to be in that they don't last 6 months, its more like 3 months, but should keep the area clear till autumn, by which time not much weed growth takes place anyway. You'll need a weedkiller watering can with a fine rose though.

I have been using Resolve,(a ready made up spray from garden centre) very good for the weeds along and in our sideway, its a huge area but one spray of this does the trick, although for different weeds it might need two goes !