It just depends on which agent you get. OP are you calling BA on the UK or US line? If the US line, try the UK line.

If you can't get it resolved, select option ?4? for customer relations and log a complaint -hopefully a BA CSR will take responsibility for getting your seat assignment.

I fully understand that, whilst it's only a short hop, it's still a selling point of BA that you can choose your seat, and you should be able to do it.

It's not that it's impossible, it's just that there has been a communication breakdown somewhere -whether the agent doesn't understand how to do it, or doesn't understand your itinerary so doesn't realise what they need to do, it's still a problem and it can be resolved.

Unless, of course, the seatmap is actually closed at the moment -but that's very unusual IME.