You could thin the populace, if you are that way inclined..tho personally..I'm no fan of rabbit..but it's a shame to waste it.
I get a few too, the don't generally cause me too much trouble, only when I set the veggie garden. Then I have to put up a little fence..nothin fancy just a short chicken wire job.. maybe you could do this round your perimeter? It doesn't have to be too tall, so is quite easily hidden by plants etc. Check for burrows too...they have a tendency to dig in my flower borders..
Thankfully..I don't get as many as you..!
(if you want a partridge to make a game pie, let me know..i got them too lol)