Regardless of what the status of hostilities in the Middle East will be at the time of your planned holiday, IMHO the risk calculation has changed dramatically. When travel is required is one thing but discretionary travel another and as the UK Government and others are strongly advising against such travel, then I believe this gives you the right to cancel. BA will tell you they see it differently and have disempowered their agents to make any decisions on this, but that changes nothing.

EDIT: If it were me, I would be writing to cancel the arrangements and quoting the FCDO advice. If BA do not refund it, then proceed to your travel insurance. Your insurers would not cover you for travel against FCDO advice, so when that advice not to travel kicks in then they must, logically, allow the cancellation charges. But, even if out of pocket, I still would not be going anywhere near the UAE for the moment.