identify thief of tulip flowers!

The rabbits that can get to them have mine!! and leave them lying about. Could rabbits get in.

Sounds like my chickens who have decimated my bluebells by snipping the flower heads off. They don't even eat them so why do it?
Then I saw one pecking away in the middle of the base of a plant. Could be insects? Baby slugs/snails? They just wanted the flower out of the way for access?
If the stalks are snipped cleanly it's birds imho.....

We live near farmland and at the edge of a forest so it could be rabbits (but not seen any droppings); possibly mice but never seen any.  Slugs do nibble some stems but these have been cleanly cut/nibbled.  What was funny was that the flower heads seem to have been gathered together and disassembled, as though some animal/bird was after something particular. I've put some tree branches among the pots to try and deter birds.