Got foxes. Lots of foxes on our farm. A female took up residence under our neighbor's vacation cabin and raised kits there this sumer managing to feed them entirely on the neighborhood's chicken flocks. Our next door neighbor lost every bird except one hen and it wasn't unusual for us to walk around our pond and find feathers from everything from Guinea fowl to somebody's white chickens. We don't have white chickens.
The cabin owner finally came to his cabin for a holiday and we got to tell him about his non paying guests. We had seen the female several times, she is a big beautiful animal and have found her kit's footprints around our coop. He knew about her but hadn't been able to catch her in the open long enough to shoot her. He said there were hundreds of picked chicken bones under his cabin so those babies were well fed.
I am certain the reason we haven't lost any of our birds to a fox is 1) we do not free range 2)we have farm dogs who LOVE to torment varmints, kill and eat them if possible and 3) we have a hot wire running around our coop and run.
Our coop is also metal clad on all sides and sits on a concrete slab and yes, we have a livestock grade hot wire system around the run at heights varying from 5 inches to 8 inches, and around three sides of the coop. Like I said, we have found the kit's footprints in mud around the fence so they are scoping our area out but.....no takers. We plan to add a second line at the top of the run to prevent anything from climbing. My fence panels are kennel grade chain link.
So foxes will dig and yes, they will climb. You can always bury wire as suggested but my best suggestion is go hot wire. If you have pets, yes, they will test the waters and yes they will get zapped....never to come near those birds who they are sure are armed and dangerous. Same with foxes or any other wild animal that sniffs around your coop.
No hunting....but can you trap nuisance animals? First off. Fox are very hard to trap with a live trap. I talked to a conservation official getting permission to rid the neighborhood of our unwanted guests and he told me they call them foxes for a reason. You can't outfox them with a live trap. He suggested using foot traps but gave us permission to shoot the fox and her kits as they have proven themselves to be nuisance animals that kill livestock.
So that is my final suggestion. Do you have conservation officers in the UK that you can call to have remove the fox from your area? I'd still go with a hot wire and a good tough dog but I'd also contact them for help and suggestions. I know things are done differently in the UK then they are here, so that might be the place to start.
Good luck. Gorgeous coop BTW!