Yes it works: try + 202 578 0742. If you haven't already done so, suggest you get your local BA reservations office to book [and price] the itinerary. Then fax the locator to BA in Cairo [+ 202 574 7674].
If you're not planning to be present when paying for the tickets, you'll be asked to fax the last 2 pages of your passport, together with an authority to debit your credit card.
BA Cairo can hold the tickets awaiting collection when you are ready to commence travel.
It's really that easy.