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"muh UK has no wildlife/ no wilderness"
kek. Even my area of sussex, the downs, has large swathes of woodland with lots of deer, rabbits, pigeon and squirrel. there are many forests that you could easily hunt and live in for a while before being caught.
We have an overpopulation of deer, so hunting won't be a problem.
Just go to the Lake district, Northumberland, Or Scotland. Lots of hidden wilderness.
The only trouble you may have is trying to backpack with a crossbow and animal traps. you could have a take down recurve and easily go backpacking with that.