Thank you!
I have been a frequent (weekly) flyer for many years, but never spotted this great forum.

Yes, we would have arrived on time in London with the IB routing
BA/IB claim that AirEuropa should have known that the second leg was operated by BA and not Iberia.
The FIM reservation was invalid according to BA/IB as no (Interline?) agreement exists between AirEuropa and BA to guarantee payment for the flight and therefore AirEuropa is responsible for the mistake.
However, our counterargument is that Iberia is the marketing (selling) party and accepted the FIM booking by AirEuropa and issued the boarding passes. Therefore they are as much at fault for their reason given as IB staff didn't spot the error either.