apparently (well according to my mum) you are allowed to shoot them with an air rifle assuming you have one( something to do with them being vermin),but please dont break up a happy home!!
aww why do you want to get rid of them? That sounds sweet! My mum had some in her garden and she used to see 2 pairs of them every day until one day the neighbours cat ate one and the other was left on its own. I felt really sorry for it when she told me! It was a happy ending though because it joined the other couple so they were altogether. I'm just soft though, not mad I promise!
Everyone appears to assume that they are the feral pigeon but I've not known them to build in a tree/hedge. If they are, once the eggs (2) have been laid prick them with a needle. They will sit on them but not hatch.
If they are the wood pigeon (with a white neck patch) leave them alone.