You've, ah... sown yourself a real problem. The wild flowers, as you are finding, propagate from seeds spread from the flowers. Some of these seeds are very small and they are all very hardy. I would suggest spraying the area with an environmentally friendly weed killer now, and then again in the spring as early as you can, but at least 2 weeks before sowing vegetable seeds. Even, then, you'll have to pull up the occasional wild flower...
Best of Luck!
