Splitting hairs I suppose it could be argued that BA do still operate 'virtually' from BHX as a codeshare on BE flights to DUS, HAM, STR and MXP. All of these are bookable on the BA website, which are then ticketed by BA and issued with a BA flight number - although I wonder how many people actually do book on ba.com for a flight from BHX to HAM that is operated by BE?
So why not also add a BA flight number to an IB BHX-MAD? IB flights from MAN and GLA have BA codeshares on them - you would think BA would rather route MAD bound pax from these airports via their flights to LHR but they are obviously happy to allow IB to take a share of these pax. With the amount of South and Central American connections at MAD and a relatively healthy potential for O&D traffic (as well as BA's thoughts to make MAD a secondary hub for it in Europe) you would have though BA would like a slice of the pie at BHX on this a route. ATNotts is therefore absolutely right.