What's happening to my seedlings?

I've got a seed bed with leek, parsnip, carrot, beet, spinach and fennel all coming through nicely - couple of inches tall and looking really good.  But inspected them today to find that some of the beet, spinach and fennel were lying on the earth.  Not uprooted, look like they have been cut off above the root.  Also looks like the earth has been disturbed.  Any  Ideas what this could be?   Will I lose all my seedlings?   

I've had a Google - they sound dreadful.   I'll have a dig around tomorrow to see what I can find. 

I've been having a dig round witha teaspoon, and today found a small brown caterpillar.  Google images show lots of pics of cutworm, and I think what I found wasa young one, as it was small, brown and straight - pictures of older ones seem plump and all sorts of shades of grey and brown.  Only found one though, so ill keep poking, and watch out for further damage!