The Fenn trap is legal. There are however legal requirements for their use. They must be covered, as in a tunnel which stops birds (or our chickens) stepping on them. If the tunnel is small enough the size of bird that could enter is so small the trap will not spring. I doubt a blackbird could set one off either. Only big rats are heavy enough. They must be checked every day and anything caught but not killed despatched humanely. I accept that being caught by one and not killed outright for any period of time is not humane in itself. But I won't use poison.
The Fenn MK6 has 6" jaws and is an incredibly nasty thing. Break your fingers no problem and is really just for Mink. If it is covered as required by law a fox will not stand on it. But I have been told of poultry keepers nailing Fenn 4's to the top of posts. Buzzards are attracted to the shiny plate and lose their legs, which is highly illegal and extremely cruel. If the practice continues it is probable that snap traps like this will be outlawed.