Yes, particularly Section 4 of the Animal Welfare Act 2006 which prohibits ‘unnecessary suffering’. In its ‘Wildlife Management Advice Note‘ (published in 2010 and revised in April 2019), Natural England says of the Animal Welfare Act 2006 that “Although the Act focuses on domestic animals, it also applies to wild animals while they are being held captive”. The note specifically highlights the example of birds caught in cage traps (though it equally applies to eg snares), stating that “Under the Animal Welfare Act, leaving an animal in a cage trap without food, water or shelter for a period of time, so causing it to suffer unnecessarily, may be an offence, especially if the period of time it was left untended exceeded that of any relevant licence conditions or guidelines.”