These all work but nothing is foolproof
PIR water jets, pain in the but if you forget about them
Electronic cat deterrents, some cats are tone deaf
Dogs, unless the are out 24/7 the cat knows when they are out
Cat in the loft, not all cats are territorial and or alpha cats
Rubber snakes, you have to mind and shift them
Bell on the collar, ask all you neighbours to fit a bell on the collar to alert pigeons
Air rifle, cats make far too much noise when you hit one and you may be reported
Cat traps, I have found them the best, caught the cat and relocated it as I don't have the heart to kill it them :-/