This comes up every so often I think.
The ways that I know of are:
1)
classic.checkmytrip.com - on the e-ticket details, but it's not 100% reliable (information may be blank, and if the e-ticket isn't issued then it won't be there).
2) Apparently there are iToy apps that hold this information, including one called "myfllights"
3) Using
matrix.itasoftware.com to try and emulate your ticket (bit hit and miss though, especially if a long time after booking).
4) Ringing up BAEC and asking for your "fare basis" code.
Any others? I guess a well organised traveller (which I am not) should record their fare basis when making non Avios bookings on BA.com, especially if using UuA.