When did you plant the radishes? Did you thin them as they started to grow or are they tightly packed together? In the ground or a container? Have you kept watered?

They certainly don't like to be crowded. Could they have had too much nitrogenous feed? If you've been feeding other things nearby, it could have put the nitrogen levels up quite a bit as the feed spreads through the soil. They need to be kept 'well moist' but not wet, sunny (but not too much or they'll bolt). And ... did you prepare the drill(s) before planting? Personally, I wouldn't even think of replanting - just thin them where they are.

Young, tender radish leaves add a nice bite to a salad, so the thinnings won't go to waste. You also say in a previous question, that the soil is very peaty. That may not be a problem, since I have grown many radishes in peat-based potting composts, but if they dry out a little too much between soakings, that will supress root development. Lack of potash will also prevent good roots. There is a possibility that the plants are too old to produce roots now, even if conditions improve.