Help - my tomato seedings are disappearing!

For the first time ever I've managed to grow my tomato plants from seeds and I've now potted them on into individual pots.     

I don't have a cold frame or greenhouse but for about two weeks after potting into individual pots I brought them in each night and put out each day to harden the plants off and all seemed to be going well.  I've now started leaving them out at night and my problems have started.

Each morning I find one or two of the plants have completely gone except for a centimetre or so of stem.  The problem doesn't seem to be affecting my chilli plants which are at the same stage of development (although that said one does look a little 'battered/sorry for itself'.  The more mature of the plants - those that are perhaps 6 - 8 inches tall with plenty of leaves seem to be ignored.

I expect someone is going to tell me this is slugs or snails but I can't find any trace of silver slime anywhere near the pots but is this what is causing the problem?  I did wonder if it was birds having a peck at the plants first thing each day - we do have a problem with pigeons.  I've also had for the first time, lily beetles but seem to have got them under control but the seedlings are still disappearing.

All suggestions as to a. what is causing the problem and b. how to deal with it would be gratefully received.