I'd be furious if anyone came into my garden without permission! (I've got bolts on the back gate, anyway - so they can't.)
Does the neighbour's cat often come into your garden, Carolebarrel? Do you know where it gets in ...? If you do, I've got a great tip for you ...
Get a man - any man will do - to pee around the place where the cat enters. Cats hate male urine, and won't step over it! (Make sure he doesn't let loose on your flowers though, as most plants hate male urine too!)
If you don't have a handy man, perhaps you could advertise - 'Wee deal for adult male - 50p a pint.' I'm sure you'd get lots of replies!