just done abit of revision now as per usual the government has no idea what it is doing and has made this bit of legislation
"The polecat is listed in schedule 6 of the 1981 Wildlife & Countryside Act, and Schedule 3 of the 1994 Conservation Regulations.
Under these laws, certain methods of taking wild polecats are prohibited.
These Acts prohibit the deliberate or intentional setting of traps, snares and so on for polecats without a licence. "
although if you accidentally trap one whilst trapping vermin or a pest i.e mink. then yes you can kill it using a suitable firearm