Oh don't get me started here

So, my understanding is that domestic transfers between T3 and T5 for priority passengers ( definition of "priority" is unclear), can have minivan or even executive car transport between the terminals. This is something to do with easier / not required additional security. It's clearly subject to vehicle capacity.

For international transfers, even in F, as GGL, I have had nothing like this happen at LHR, even when I was on a very tight connection, which I then missed, costing BA EU Compensation in my case. I understand that in this case it would require a trip via T5C to clear security again and it's not really been feasible in most cases, thereby shoving you through the usual FC non-premium experience.

I have it on good authority that BA is looking to add to the capacity in this area, so more premium passengers will get the treatment on domestic transfers, and that the international transfer approach is being looked at.