More information here:
https://www.flyertalk.com/forum/brit...nnections.html

but the short answer is that's done in priority/hierarchy order, and it wouldn't surprise me if at a quiet period the transfer was allocated to Silver passengers. I've had 4 hour connections and been offered the transfer, and delayed 70 minute transfer time and not been offered it. So not predictable. 40 minutes for the bus transfer is at the top end of the scale for me, sub 30 minutes is usually possible. The jag transfer can take 15 minutes.