Slugs, the small greyish brown ones are the usual culprits.

Woodlice like to nibble Daff flowers in my garden! :o((

I've also seen birds [pigeons in particular] peck at them and the pheasant that visits is partial too.

Our Minister once ate a daffodil flower just to attract attention. But you would probably notice if it was him.

Just to attract attention??? Was it during a particularly boring sermon? ;-)

In my garden the pheasants eat them!