Yea, I've only done this once last month, but it took a while. This was VIE-LHR-RDU with LHR-RDU already cleared.
The agent initially said it wasn't possible, or that I needed to be on a full fare. I asked her to please check with her supervisor or rate desk etc., she comes back and says OK we can do it. I'm then put on and off hold for at least 10-15 mins while they process it.
Everything worked in the end but it for sure required a lot of pushing and pulling and help from the rate desk and what not. Definitely try HUCA.
And the fact that this is a short flight or that BA's short haul business class sucks is irrelevant and beside the point.