Yes it legal to kill the little buggers....and pigeons and other pests.
Avoid poison 'cause the neighbours cat will just eat it and then there is all sorts of problems,plus there's a good chance you'll kill off the local 'nice' birdlife as well.
Sonic stuff is a waste of time if you just want to scare them...if you can trap them thats ok.
What you need is an air rifle but make sure you shoot with something behind them to stop the shot ie from an upstairs window when they are on the lawn rather then from the garden when they are sat on the eaves.