It may be they're not getting enough light, or have been exposed to direct sunlight, or its too cold on the windowsill overnight - we've had some cold nights, so move them off the windowsill overnight and replace the following day.

Hi there,
I agree with bamboo, are your seed trays/pots of seedlings covered?

Make sure they are not overwatered, the combination of wet and cold is a lethal one for seedlings.
If all else fails and you end up binning the lot, re-sow. There is still plenty of time to do so. I have only just started with my sewing, and allthough it is tempting to sew everything, I start with brasicas, as these tend to take a while to germinate, and then move on to other less troublesome seeds. When it is a little warmer, I sew direct into ground or planters.

I wish you happy growing.