How to recognise carrot root fly
Lots of brown tunnels in your carrots is the result of carrot flies. They lay their eggs around carrots and parsnips. When the eggs hatch, the larvae bury down into the soil and nibble on your carrots/parsnips.
Prevention
The very best way to prevent this is a barrier of horticultural fleece - simply lay the fleece over the top of your row of carrots/parsnips and secure well at the sides. It is not fool-proof, but should keep numbers down enough that you get a good crop even if the problem is rife in your garden.
You can also try planting onions and garlic chives in and around your carrots as the carrot flies don't like the smell.