I wasn't aware of BA's policy of not using the stairs. It does makes sense if upper & lower bridges are attached.
Many A380 fly into airports that are setup for A380 traffic but they don't always get the gates for it. I've been on a few where the few gates were in use already (even a few times by other types of aircraft) and deboarding took a long time. This is of course becoming rarer and rarer as airports modernizes as airlines (Mostly EK) spread the use of A380s across the globe. I honestly never thought I'd see an A380 to PRG and other less popular long haul destinations.
It does depend on how long it takes the upper bridge to attach and CW/WTP passengers to disembark, but upper deck economy would typically be off before half of lower deck economy.
BA doesn't operates the A380s to any airport without A380 capable dual level bridges. Some may only have two (for 2L Main and 1L Upper), others have three (1L/2L Main and 1L Upper) but upper deck passengers will always board to the upper deck. And they don't allow passengers to use either set of stairs.
In fact I don't know if any airline operates A380's from gates not capable of connecting to the upper deck - perhaps EK.