It's said that there are two main reasons for this sort of deformation.

1st, the ground has has too much manure and is too rich.

2nd, the grond is very stoney or hasn't been dug over thoroughly enough.

"seph..." wrote

They all seem to be suffering from the same thing and I would hazard a guess
the ground was not dug over and loosened to enough depth before planting or
it may be your ground packs down hard easily. Carrots like a soft soil so if
you have clay it needs lots of organic matter or sand to open it up.
Alternatively make a raised bed.

-- Regards
Bob Hobden
W.of London. UK