I don't know which fern species it is but it is beautiful. Is there a reason you want to kill it? Dyfa, are you in the U.K.? Wales? If so I would beg you not to destroy these. Our native plants are under threat enough as it is and dry stone walls form an important and unique habitat for plants and animals. The only reason I can imagine for getting rid of this lovely fern is if you have to renovate the wall. This site might help you identify your fern.

Yes in North Wales. As the pictures show, it grows to close to the house walls causing dampness, but also the roots dislodge the stones and collapse. What is the best way to stop their growth and get rid of the roots?

The ferns grow there becasue of the damp, they don't cause it. I can see you have some Harts Tongue fern and Maidenhair Spleenwort there too. It's clearly a perfect fern habitat. In North Wales trying to eradicate ferns is going to be a hiding to nothing. I think the only solution is going to be expensive. Getting the house damp proofed and digging out that concrete around the base of the house wall and moving the dry stack wall further back. But that would be major earthworks. Just removing the ferns won't solve your damp problem. You really need a builder, not a weedkiller. But I would get in there and remove the Sycamore and Ash seedlings and get the grass further back from the top of the wall. That will be holding moisture. I commiserate. I also live in an old house with no DPC. Damp is a way of life.

There is no damp yet, but I just want to keep on top of the vegetation so that it does not touch the walls and therefore moistness and dampness. It is a long term plan to move the wall further back, but only just bought he property so it will have to wait. I'll definitely remove the sycamore and ash seedlings and remove the grass from the top of the wall. Would roundup have an effect on the fern growth?

You'll have to find that out for yourself. I can't, in all conscience, advise on killing these beautiful native plants. To stop the ferns touching the walls (which wouldn't cause damp in a sound wall anyway) just shear them back periodically.

OK, thanks for your advice, much appreciated.

Call a garden club or native plant society. They'll want the plants, or they'll know someone who does. Good luck!.