If you want to use snares in this country they must be free running. Snares which lock ( ie get tighter as the animal struggles ) are illegal - and rightly so.
It's also illegal to set one and fail to return within 12 hours and to set them around badger sets. You might find if there's common land around that you'd have no problem with snare setting - or you could ask a local farmer.
Modern snares are brass wire and cost about a quid each. I've made my own from fishing net washed up on the beach, I pulled out strands and braided them in sixes making sure I had enough to make a loop wide enough to put my fist through plus spare for fixing. Pegs from diftwood about eight inches long, teelers ( a thin support to keep the loop positioned correctly ) from twigs.
You should set snares along a run, look for bottlenecks such as spots where bunnies have to go under fences, between a couple of rocks etc - anywhere than funnels them along a restricted course. Two fingers high for the base of the loop using the teeler to steady it. Don't disturb the run itself, always approach it from the side.
These snares won't kill - they just hold. Kill the animal before you remove the snare ( assuming you want to eat the animal ). How you'd remove a fox or weasle without getting bitten I don't know, I've only ever got rabbit.
Of course when you come back to check them, someone else will have nicked them and set them up else where - or at least that's happened to me a few times.
Realgar