Nope you're all wrong - read the general licence gumf!!! It does say to prevent damage of crops, but also allows you to controll corvids to protect songbirds, or prevent a hazard to human health (crow poo and saliva on golf balls counts!).
I can rarely be bothered to read sporting rifle, but clearly remember an article in there where they were shooting crows for stealing golf balls - apparently there's even something in the general licence literature that covers controlling "vermin" classified species that infringe on recreational activity!
Murder away pal, though I'm assuming you're able to identify a crow regardless of previous posts - in case not here's a key tip: they look like crows!!!!