catsen
If you are near an airport served by BA, I suggest that you go to the ticket desk, show them your airline ID and ask for their help. They can pull up the reference in seconds. I know people who have done that. I can't find any way that you can do it on line or by phone (for obvious security reasons).
The reason that I asked who you bought the e-ticket from is that many airlines send an e-mail with the reference number (BA certainly do). BA always send an e-mail for any listing or booking change, but I suppose that will depend on whether they have your address.
Best of luck
Dave