The fox is sometimes referred to as vermin, but it is not, and never has been categorised as such by the Department for Environment, Food and Rural Affairs (DEFRA).
Foxes are considered mammals in UK.
Any foxes, moles, and mink that you catch are protected under the Animal Welfare Act 2006. You can be jailed and fined up to £20,000 for causing unnecessary suffering to an animal.
You can’t use the following for foxes, moles, or mink:

• self-locking snares
• bows and crossbows
• explosives other than legal ammunition for a licensed firearm
• live birds or animals, as bait or live decoys

Failure to do so could mean you face a jail sentence of up to 6 months and a fine of up to £5,000.

Additional read:
Hunting and Shooting Wildlife
BASC – Night Shooting Code of Practice