EDWARD COOK says:
If you are an accurate shot and able to consistently hit a rabbit in the head, then a standard air rifle delivering up to 12ft/lbs is more than capable of killing cleanly at 40-50 yards.
You can stretch this distance if the rifle is rated above the 12ft/lb limit, but it will then have to be held on a firearm certificate.
My old Weihrauch Mk77 has killed thousands of rabbits over the years, and it still kills well enough now. One of the beauties of hunting rabbits with a little air rifle is that it teaches you an amazing amount of fieldcraft, including the absolute need to get in close to your quarry before attempting a shot.
Regardless of which air rifle you use my advice would be to spend as much money as you can on buying a decent telescopic sight because then you will end up with a top notch set up for killing rabbits.