Hi :wave:
We're both rubbish (really, really rubbish - you should see our house) at DIY but we managed to build a run for our rabbits and a walk-in aviary run for our chickens and for us it was the most cost-effective way, plus it meant they could be completely customised for what we wanted. We're in a similar position to you in that our garden has hedges on both sides and we can't really rabbit-proof it as we have visiting hedgehogs. We live near open farmland and get foxes in the garden during the night and sometimes during the day, and we also regularly see buzzards nearby.
Our rabbits don't have a walk-in run but I've posted a picture of their run below anyway just for the idea, as it was incredibly easy to build. It consists of a set of welded mesh boxes, which we made using welded mesh panels available from Wickes, attached together at intervals of 2-3 squares using J-clips. The wire is so stiff, we were able to make the boxes without even needing to use any wood. They have a welded mesh floor, which is buried under a layer of soil or turf. The boxes are attached together with Runaround tunnels, which ultimately lead into our conservatory (our rabbits are house rabbits). When we're out in the garden for a long time, we unroll a temporary fence around the lawn on that side of the garden so the rabbits can have a bigger space to run around in and when we have time we're going to put a permanent mesh fence around that part of the lawn (with little doors that we can open at night for the hedgehogs!!) and let them access it under supervision.
Our chickens have a walk-in run on concrete slabs. First we levelled the ground and laid the slabs (with a mesh skirt around the edges for added security), then we banged posts into the ground at each of the four corners (this was the hardest part). We also laid wooden posts on the ground between them to make a base. We built wooden frames to fit between the posts and we bought a big roll of welded mesh which we attached to the frames using this really amazing staple-gun thing which we got from Screwfix (we started off hammering staples in but that took forever - with the staple gun it was easy and quite fun). Finally we nailed the frames to the posts, the base and each other to make the walls. As you'll see from the photo, the whole thing is a bit wonky, but it does the job, is secure and has lasted well.
Not sure if any of that is helpful - it's just how we solved a similar problem.
Good luck getting your set up sorted!!
Amy.
