Posted: 18/05/2015 at 07:27
I've dealt with areas like that in the past and turned them into 'garden'. It'll take time and a bit of hard work, but it can be done.
Spray thoroughly with weedkiller containing glyphosate. I'd use a knapsack sprayer to deal with that area properly. Wait until it's all died down and is brown - probably about 3 weeks. Then dig over the area thoroughly removing any roots, large stones etc. Leave fallow for 6 weeks - if more weeds appear then spray again and repeat until no more weeds appear.
While all that's happening I would be sowing and raising your own plants of perennial wildflowers in pots.
Then you can dig and rake the area again and sow or plant your wildflowers.
Always remember that weedseeds will arrive on the wind so you'll have to keep an eye out for weed seedlings and hand-weed them out, or you'll have the same problem all over again.