...and close to my patch too, I see!
I do admit to having an 'agenda' here, being (a) non-meat-eater, and (

finding blood sports abhorrent. But if you really want to catch rabbits for food, well nothing wrong with that in principle, not really a blood-sport.
But I do think you'll find it more trouble than it's worth, especially if living in Uni. Skinning and cleaning a rabbit (and checking over for parasites) is bound to be a messy job. The Downs are criss-crossed with public footpaths, and if you endanger a member of the public, ... well, figure it out. If you want to join an organised shoot, fine, go for it, be ready to part with most of your Student Loan...
As for the rabbits themselves, well I do agree, there are far too many of them, they are pests, and can be a danger to cyclists especially in early summer when there are young'uns about with no road-sense. Watch out for them if pelting down the Beacon full-tilt!