Most airlines (I fly on a couple of different ones all of the time) will allow you to bring only one carry on bag...Of course your handbag does not count.
No wonder airlines are starting to get a bit more strict with the hand luggage allowance.
your handbag DOES count with the new uk security measures. your handbag must fit into your main item of hand luggage for the security screening. there's nothing stopping you from taking it out after that though.