OP has already stated that he traveled to London in "Business class", and has no complaint about that aspect, so presumably he was in CE on BA.

But his experience with IB is classic and the same thing happens routinely for tickets and not just for the FF plan. Once it took 3 IB agents and almost 2 hours to re-issue a simple full-J ticket which had no complications (rather unusually for me). This was in MAD after a mechanical caused a reroute. Another time a difficult reissue took less time, and 1 agent, but still about twice as long as CX or AA would have typically taken. Often the agents are very nice but apologetic and powerless. They hit some obstacle and then are clueless as to how to proceed -- or must wait until the 1 person who knows how to do it is available. It seems that 99% of IB ground staff do not how to do the less frequent aspects of their job. Now IB is greatly improved from 3 years ago -- then IB agents would tell you to get lost and not bother them; now they tell you to wait, and hope you'll give up and go away on your own, or they find some loophole to justify not working further. Air Nostrum (100% owned by IB) is amazingly different in this regard, hard to believe it is the same airline (they are excellent, a rare case of commuter jets being preferred over mainline).