Hi,

Welcome to FT.

Do you have your boarding passes? [They are the most important things in proving that you actually flew on the flight - it's one thing to have a ticket, another to fly.]

N.b. everyone has a ticket number, it is just that you didn't have a physical ticket but rather an eticket.

Your ticket number should be in your confirmation email. [It will be an number beginging "125-...." if it was sold on BA ticket stock (doesn't have to be sold by BA, could be expedia, etc, etc). It will have a different number if on a differnet airlines ticket stock. [And you can fly BA with a ticket on another airlines stock, or another airline with a ticket on BA stock, just to avoid any confusion.]

If you stick you booking reference into www.checkmytrip.com it might offer you it there still (but this will disappear soon, as you have finished the journey).