British Airways are horrible for this. They do not allow knitting on ANY of their flights. The BAA (British Airports Authority) say that knitting needles are allowed in the cabins of flights, but individual airlines have individual rules and BA is one of the harshest.
You are now only allowed ONE piece of baggage, that is bagged in the hold. You are also allowed only ONE piece of hand baggage with discretion they will allow laptops to be taken as well as a hand bag. A purse and a piece of hand baggage is not allowed. It has to be one bag only.
If you want more than one bag in the hold, you have to pay extra for it and again it is at their discretion whether they allow it or not.
Personally, BA has been taken off my list of airlines that I am prepared to fly with. Coincidentally, American Airlines has the biggest amount of leg room in Economy class - a whopping 34"
Sorry that the news is bad, if you can change your flight to American Airlines, you'll be able to take your knitting on board without issue.
Also I personally probably wouldn't even bother to ask at the desk. The needles ARE allowed through security, (better to bring bamboo or resin or plastic) who is gonna know till you are in the air and whipping the needles out that you have em in your hand baggage?
If they get antsy at the air gate when re-xraying your bags (why do they need to do that?) after they were already x-rayed several times on the way, then kick up a fuss, say how expensive the yarn and needles were and ask the captain to hold them in the cockpit if they are really that scared they can be used as weapons. Tears possibly may help too =P