Okay, as far as I'm aware, and off the top of my head, the Wildlife and Countryside Act 1981 pretty much states this (on lawful killing of birds)...

''Part 1,-4: 3b: preventing serious damage to livestock, foodstuffs, for livestock, crops, vegetables, fruit, growing timber, or fisheries'' (Link) http://www.jncc.gov.uk/page-3614

So, there you have it, it's pretty vague.

It's also worth noting that somewhere in that bundle of laws it states you should only use the killing on birds as a last alturntive to non-lethal methods. (such as putting shiny discs up to scare them, or something).

So, as far as I'm aware, I'm almost sure it's not legal in your case.