OP, there's fast track immigration for passengers travelling in premium cabins (First and Business). Last time I arrived on the BA33 immigration queues were short and processing was quick. Longer queues on departure but staff with no passengers on other priority lanes processed premium pax. In my experience baggage delivery can take some time. On departure there's a cursory security scan after immigration, the main security scan is at the gate. As far as I recall there is no security fast track at the gate. Passport & boarding passes may be checked multiple times. Safe travels. Doc Copper.