might be best if you make a 60cm wide roll of chicken wire into an L shape, and then lift the turf around the outside of the run, to bury the bottom part of the L, and leave the top part sticking up around the outside of the run, so long as they can't scratch themselves on it if they go in the garden freerange? I would put a row of pavers around the inside edge too, so they're not tempted to dig out.
for the top you can buy cage mesh from wilkinsons and staple it to a wooden frame - if you do it in sections it shouldn't be too hard - then make a wooden cross shape on the top of the run to nail the frames to?
If the sides of the run are chicken wire too, be aware that it's not strong enough - even a rabbit can bite through chicken wire - you need cage mesh.