Starter flour swaps (same type)

I've always known that putting an established starter in a different type of flour, can be... slow.  What I didn't realise is that using the same type of flour (white for white) could have such an impact!

I've been using a supermarket brand (Asda) for the last year, and I've had great results.  The missus picked up some flour when I ran out, but brought back some far more expensive brand stuff (Allison's); its effectively halved the rate of the starter.

I'm guessing I can't be the only one to experience this, but as I know no other sourdough bakers in the flesh...