Seaves. Juncus rushes.
Long view - Keep cutting them. Improve the drainage.
Shorter view - as Sally says, cut them, and then weedwipe the new growth.
Weedwiping uses a bar with holes in, out of which comes the weedkiller at a slow drip, that brushes the tops of the seaves with weedkiller, whilst not getting it on any of the surrounding foliage. You use a translocating weed killer like Roundup (glyphosate), so it goes down to the rhizomes too. The purpose of weed wiping is to only treat the seaves, cos the roundup will kill anything it touches. It only works on the new growth, the old stuff is too woody for it to penetrate.
I've got to do mine this summer. I will beg, borrow or hire a tank and bar for the back of the quadbike.