Rushes on land is a real pain. I have fields that are wet but the rushes make their own habitat and make it ten times worse if left to their own devices.
My fields are quite hilly but on clay and some have underlying rock so the water doesn't drain away easily. The Rushes establish in clumps and make the surface of the field quite rutted around their bases which is great for holding water around their roots, the close way rushes grow also means plenty of shade from the sun and wind, so water sits around for a long time.
I have dug some ditches to divert away any surface water, which has some success and you really need to keep the rushes in check with regular cutting/mowing to stop them forming clumps. You can spray any regrowth with Agritox if you can find someone to do it and over a few years the field will improve drastically.
Try to keep stock out of the field when its very wet as you want to avoid it getting to muddy in there as the seeds will already be in the soil and waiting for sunlight and broken ground to germinate.