Two questions what was the variety and what is your soil like?

Carrots are autumn king 2 Mr fothergills soil just top soil and compost they are in big pots

Quote; Carrots are autumn king 2

These are termed an 'Intermediate' in ideal conditions I would expect them to grow up to 8" long

Quote;soil just top soil and compost they are in big pots.

Big pots???

I am no expert in big pots but I have grown in barrels so there is a similarity, but your soil/compost mix is all wrong!

What may have happened is; each time you watered the mixture compacted therfore hindering growth!

What you needed was a sandy mixture!

There is some 'container growing info' here;

http://www.thegardenersalmanac.co.uk/Data/Carrot/Carrot.htm

Thanks very much your comments have been very helpful

Carrots can have large tops but little growth for several reasons: 1. They are overcrowded and don't have enough space between each carrot. 2. They were sown too late. 3. They have been given too much nitrogren which means they make top growth at the expense of root development.
4. They have not had enough time to develop.
I have often found that carrots are like this in September but when left till the days are shorter in late October or November they are much larger. With a main crop variety you need to leave them longer. If you want a quick crop in a pot, use an early variety, even if you sow it late.

Thanks for your comments I will leave the rest for a month or two and see what happens