Sowing in wet conditions or wait?

I'm relatively new to growing veg (this is my second year). This year I decided to sow all my beetroot, chard, spinach and fennel successionally so I didn't end up with a glut. However the problem is that I didn't get the chance to make all my drills back when our clay soil was the right moisture. Now I find that it is either overcast or raining and the soil is permanently wet. As the plot is an open space down the bottom of the garden with only access being planks of wood I'm worried that:

a) I'll ruin the structure of the soil
b) encourage any seeds sown to rot

So, should I risk sowing in these conditions or leave it until the weather improves a bit?

Don't sow until the ground has dried out a little. If you sow into very wet ground the seeds may well rot, as you suspect.

Thanks for the quick response. 

I think that's probably the best thing to do, but it is so frustrating missing so many days. Weather this year is unbelievable. There has been such a narrow window of opportunity to so the earlier spring veg direct.  

Or covering the soil?