What's eating my carrots?

Have some nice carrots this year, however something's been chewing away at the shoulders of the root in the last week or two. Not sure what to do - harvest and store or try to prevent more damage?

Not sure what - suspect rabbits but thought they only ate carrots in the cartoons? Plus nearby lettuces ignored... Rats or mice maybe? Did find dead mouse on plot recently, but only thought they would be a problem in the winter.

Thanks

Andy

2-3mm, with crumbs around so definitely something with teeth. Tops more or less intact - whatever it is is kind of eating around them. If it is rabbits I could probably keep them out somehow.  Bit annoying as they were in an enviro mesh tunnel until recently!