The cull is legal under a general licence if there is a public health issue -
http://www.naturalengland.org.uk/Images/wml-gl05_tcm6-24150.pdf
- and I think when I was taking a sabbatical from posting there was a thread on the state of fouling on the bridge though I don't know what it came under, perhaps those who posted can recall it.
However, it is more a question of was the shooting breaching firearms regulations, there are laws on where shooting can take place place depending on what is used, and permissions needed.