Hi Antipodes,
This is a very common issue for those of us who use our windowsills. Its not an insurmountable problem. The issue is one of lack of sufficient light – usually. It is easily corrected when potting on by simply planting deep – up to the seed leaves.
I have found a simple solution to minimise the leggyness, it does not completely eliminate the problem. I place Plasticard or Cardboard covered with Tinfoil behind the seed trays to reflect the light back onto the trays. This also prevents the seedlings from leaning excessively in one direction but I also rotate the trays daily.
The ideal solution (apart from a heated Greenhouse) would be to use Growlights. But these are expensive to buy and to run.
They do pay for themselves eventually but this depends on the volume of seedlings you are raising. I use my Growlights for bedding plants and Tomatoes and Windowsills for Veg.
We need to remember that what we are generally trying to do is to grow plants at a time and in conditions they would not naturally germinate and grow. Effectively we are trying to trick nature. We need to try to artificially create a plants natural growing conditions.
Don.