The reason for this is that the UuA online booking engine often will not identify the cheapest available WT+ fare because it's a DIF fare, but uses a non-DIF fare. If you price WT+ on its own, you get the cheaper DIF. It's been a long-standing problem (appearing in various guises) with BA's implementation of DIFs.

Booking online and then doing the UuA by phone immediately afterwards is one way of getting around the problem; AIUI there may be a small downside in that the 24-hour cooling-off period is I think supposed to end when you do the UuA by phone. (But if you phone and find you can't UuA after all, then you can still do a cooling-off cancellation for a full refund, and start again.)

Alternatively, you can try to do the whole thing in one transaction on the phone.