i would go for either .177 or .22
you can get an accurate air rifle from £250 - £1250 all will kill rabbits out to 45-50m if you are a good shot
here are the most popular rifles not in any order on here:
spring air rifles:
weihrauch hw77, hw97, hw95
air arms tx200, prosport
pcp air rifles:
air arms s410,s200,s510
bsa r10,ultra
weihrauch hw100
daystate mk4,huntsman,airwolf/ranger
atb
scott