Killer cat!

Since I lost my lovely Pushkin, other neighbourhood cats have decided to encroach upon our garden. Our two Abyssinians, Mario and Luigi, don't go out in the garden yet - I want to make sure that they are 100 per cent certain to come when they're called before they do. (They're pretty good, so it won't be long.)
But in the meantime, the other cats are making themselves at home - and wreaking havoc. Hardly a day goes past when I don't find a pile of feathers on the lawn.
I've always fed the birds in my garden, all year round. When Pushkin was alive, he would catch the occasional fledgling, but not in huge numbers, so it didn't deter me. As far as I could see, the benefits of feeding outweighed the risk of the occasional death.
When I heard people blame cats for the decline in garden birds, I'd think they were exaggerating (or anti-cat).
The RSPB says that cats are thought to catch around 55 million birds per year, but they add there is no evidence to show that predation by cats is having any effect on bird populations UK-wide.
However, the amount of damage these invading cats do is really frightening. One is a big fat tabby, the other a portly black and white cat. There's an occasional ginger chap, too. You wouldn't think they were capable of walking five yards, let alone catching anything.
Has anyone got any bright ideas as to what I can do about this? Apart from protecting the bird life, I'd like to deter these cats from coming into the garden anyway - I don't want my boys to have to fight for a space on the lawn once they start to go outside.