Is the shed reflecting heat on the herbs? What fertilizer did you use (it may have been too strong, or caused temporary leaf burn if it got on the leaves). Usually herbs don't need fertilizer--that just leads to lots of lush foliage and less taste.
Sorry to not be of more help.

To add to what marlin has already suggested, were these indoor plants you moved outside? If you don't give your plants a chance to acclimate to the outdoors or "harden off," they can die or very nearly die. I liken it to us in the middle of our coldest winter weather (for me that is subzero degrees F and snow) going to the Caribbean. The sun, winds, and temperature of the Caribbean might be too much for us. Moving an indoor plant suddenly outdoors is much the same shock. Check out the link below.

FataMorgana

Here is a link that might be useful: Google - Hardening off

Can you tell us which herbs you are growing? What medium are they growing in?

There are several of things which come to mind.

Firstly, you may have overfed them. If they have only just been planted out they don't need feeding yet.

Secondly are there Tom cats wandering across your allotments? They can burn plants when they spray mark their territory.

Thirdly, has the shed been recently painted? If you used old fashioned creosote that can affect nearby plants.

Fourthly, how often do you get down to the plot? Plants in containers are sometimes not a good idea on allotments since they need much more frequent watering than plants in the ground.

And finally, as FataMorgana asks, were they hardened off?(This means something a little different in the UK. We need to get our plants used to wind,rain and cold - not hot, bright sunshine!) We are still getting cold nights and the new plants might be suffering. Basil especially would curl up its toes immediately if you put it out now.

Just a few suggestions from a fellow allotmenteer. Hope all goes well with it.

Hey just want to thank all who responded with advice.I should have hardened them off longer me thinks after reading all your kind advice.lesson learnt.