Carrot root fly grubs. The flies get in when you thin the seedlings and are attracted to the smell of carrots. There is nothing you can do to the affected ones but the flies cannot fly above 60 cm so carrots grown in raised beds don't have a problem. Next time you grow them, put in marigold plants as they tend to mask the smell of the carrots.

I'm not exactly convinced that they can't fly higher than 60cm Cammomile... I've know folk that had high netting around their carrots and the flies still found them.

I grew mine in a raised bed with a polythene sheet around this as well, Munro, and the blighters still infected the plants. The raised bed was 1 ft. high, and the sheeting was a further foot, so they must have been very athletic carrot
flies! Don't believe anyone who tells you they can't fly above 6''. Planting Marigolds/tagettes does help, as Cammomile says.
Try doing what Monty Don on Gardeners' World does--scatter the seed over a wider area and make sure they're sown very thinly so that you don't have to thin them out. I've tried it this year and so far, fingers crossed, the carrot plants seem to be unaffected. Happy growing! Annie (Cumbria)

I've yet to find a text book that says they can fly above 2 foot. Anyone with netting above that height couldn't have secured the netting around the base, so the fly gets in that way. Or gets in when the netting is removed for thinning.
Simple things like thinning and weeding on a cool dry evening, as opposed to bright sunlit days, and removing the thinnings help.