Alan, we grow carrots in plastic buckets with the bottoms drilled out. They stand in watering trays on a shelf, about 2ft off the ground to deter carrot fly.
I use half bought compost, and half own compost, sometimes with a bit of garden soil, to make some sort of balance.
I rarely feed them, but they do need regular watering! They usually end up about the size of an average thumb, but we take them much earlier than that, as just a couple chopped up make a salad just fabulous!
I've done this for several years, and not seen a fly anywhere!