It would appear not, since the attack has already started (last Monday) by the bombing of strategic sites within the no fly zone. This is apparently done in self defence as they may be a danger to our troops when they go in. I think a declaration of war on our part would have to receive the Royal Assent in the same way as an act of Parliament would. This is a formality as the monarch never refuses to sign them.
As the Queen is technically the Commander in Chief of the British Armed Forces, the order to attack comes from her. But this is just one of the powers the monarchy has in the unwritten constitution that in reality are conducted by the Prime Minister / Cabinet.