Firstly welcome to FT Flock1

Each frequent flyer program has its own rules regarding retrospective claims for miles - so you will probably get a better response asking your question in the BA Forum

A couple of things to consider:

• you would have received an email from your travel agent/airline with details of your e-ticket; this should have included the e-ticket number. If you no longer have the email, perhaps you can contact the travel agent and get it re-sent
• your "ticket stub" is presumably your boarding pass; in my experience these never show the ticket number, but are evidence that you took the particular flight, on the particular date, in the particular cabin class
• with 20/20 hindsight you should have added your BAEC number to the booking when you booked (isn't hindsight great?)

Good luck