Today I spoke with both BHX customer service and HM Immigration and Customs about my experience on Friday night...
To be fair, both were very polite and both promised action. The slothful T2 to Long Stay 1 car park bus service will be investigated; however, the HM C&I chap described a number of possible improvments such as 'fast track' processing for scheduled airline passengers (I'm uneasy about that - queue jumping on the back of a business class ticket seems immoral to me) and an increase in staffing levels.
But, like many, they're stuck with staff budgetary limitations, it seems.
Thanks anyway to the BHX folk who returned my calls!