Well, after 3 months waiting in vain for their oft-promised text message confirming my registration and toing-and-froing of complaint letters, I decided to do a little experiment by sending a text for requesting a ticket and lo-and-behold, to my surprise, it worked, replying with a 2-for-1 ticket (which I was unable to use that week).
I have since used Orange/EE Wednesdays successfully a number of times.
They do not offer an actual explanation as to why this went wrong but do admit that it was due to the transition from Orange to EE and that a number of customers were affected. I'm pretty sure they failed to take into account that some Orange BB customers do not have an Orange/EE landline.
Still, they did recompense me for all the extra cinema tickets I paid for during this period by giving me free BB.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 19 Meg WBC