wet area of lawn with rushes growing

Gerry, Help!! I have killed off some of my lawn for a shrubbery border (54ft long x 17 ft deep). I used Round-Up about 2 mths ago as the local garden centre said I could plant again after 4 weeks. It has killed off all of the grass but due to the volume of rain some grass is growing back and there are alot more rushes after appearing in the area. There was always a few rushes in the area but the lawnmower always kept them down when cutting the lawn. It is at the back of the garden and I wanted to put a 3 tier shrubbery, with large evergreen shrubs, then a layer of medium shrubs and then a layer of low growing ones at the front. What can I do to get rid of the rushes as I have weed blanket to put down and I’m worried if I put the weed blanket down over the existing rushes they’ll continue to grow and puncture the weed blanket.