Perenial weeds are difficult but not impossible to get rid of. We've just got rid of about 1 acre of nettles. It sounds like you have less space than this so there is hope, and a variety of options:
1 - chemicals - You can use a DIY product for killing perenials or something more "agressive" like Grazon. These require you to keep animals and children away from a aweek or so. They can be very dangerous. Another downside is that you have to hit them at the right time - when the nettles are about knee high - just before they flower/seed.
Something like Grazon seeps down into the root and kills it, although a really deanse area ( i.e.e one you cannot walk through ! ) may need a second application the next year
2 - Burner. You can get a propane burner to kill them. These are geat as the nettles can be tackled as soon as they appear. The burning of the top row of leaves kills the cell structure and stops that root growing any more - without the leaves it dies. An advantage is that you don't need to keep animals away afterwards. The downside is that the burner costs about £60 plus the bottle - cheap to run once you've got one though. Don't go for these £25 burners that go on a disposable gas bottle - they don't last long enough. If you want one, search for "weedwand" on the web, www.gonegardening.co.uk do a couple.
3 - The third option, and often the best, is to pull the weeds up by hand. It doesn't take as long as you think. Wear long sleeves and buy welders gauntlets ( they are very cheap (£3) elbow lenght gloves ). Burn the foliage once its lifted. try to pull as much root up with them as you can. just proceed one stalk at a time, they come up fairly easily,. Let them grow to about knee high first so you can easily grab them. You may have to repeat this next year but the roots will be very shallow. The real benefits of this method are cost, environmentally friendly, and you never know what you'll find looking at your garden so closely !
4 - Another option is to regularly cut them down, strim them every time they get to ankle height and eventually they give up, this will take a couple fo years and overall is more effort than lifting them