The quickest and most effective way is to spray it with Glyphos and reseed
But Laura has said she wants to keep her land organic. Glyphosate is not the wonderful, no residue, happy-clappy weed killer we are taught to believe.
We are shortly going to convert an area of our land for wildflowers, once we get the tups off next year. We want though to grow plants which would normally grow on this area, rather than the ubiquitous oxeye daisies, cornflower and poppies. Half of our area is dry and well drained, lightish but fertile soil, the other half is clay, boggy and poorly drained.
Without being able to see into the future, a few years back we oversowed with clover, which has thrived and is busy increasing the fertility. Hmm. We never use chemicals on our land, so it looks as if we'll need to work with the clover. Existing wild flowers include buttercups, daisies, self heal, ladies bedstraw, various tiny things and a few orchids.
It's going to take a few years to establish the grassland with appropriate wild flowers, but we'll have fun experimenting as we go along