It DOES count as a carry-on, but I think you are allowed one carry-on and one personal item (purse/laptop bag), so I think you would probably be able to act like London is your purse and then just stick your carry-on in the overhead bin. Every time I have ever flown with Rory no one even noticed I had a dog and she was in a bigger carrier, so I'll bet, especially if London is quiet, it will be similar for you.
