Also, looks like MNL-DOH-LGW on QR/BA is available on the 23rd. But AA sometimes shows phantom award availability, so you would need to verify via ba.com.
If there are no options for getting to LON from TYO, then I think that you have to argue to BA that requiring the traveler to fly to TYO only to be stranded there is non-sensical. And would Japan even permit a foreigner to fly in without confirmed connecting travel?