Happens all the time. I'd be happy to book separately, knowing there is a bit of a risk, but if the connection to the OtherCity is over (say) 2 hours you'd probably be ok. So long as you can stay airside (so hand luggage would be good), Flight Connections will probably be lenient, particularly if you have a bit of status to flash and the cause of the delay was BA related. It's definitely OK to put your BAEC number in, in fact it will assist if you do have an awkward conversation explaining the last minute change to see your mistress / football team / Formula 1 shindig or whatever. You'd still be chucking money at the airline and they don't need or care to assess your moral fibre before accepting your filthy lucre.