While there are instances when the relationship with Baggage & Logistics TUs breaks down, that's not the sole reason for a slow delivery. The reasons, in my experience of having worked with those teams in the past, are several. In no particular order:

• Layout. If you land in T5B, C and remote stands in the 590 range (where the fuel farm is) there is a rather long drive from there back to T5A. The speed at which the Linde and Charlatte tugs that drive the dollies with the baggage bins can go is around 15 miles per hour, less when they need to go uphill (there are a couple of ramps). Result: it can take less time for passengers to take the train and clear immigration than for a dolly to drive to T5A. It's not unreasonable to see a 40min drive time, especially with traffic.
• Congestion. Linked to the point above, but there are a couple of access points to drive into the bag room (on the other side of the hall). There is a dual carriageway, there, that is used both to offload the bins onto arrivals and to access the laterals where the bags are loaded. Traffic can build up, especially in the morning. Those trains of dollies aren't exactly nimble or manoeuverable.
• Staff shortages. Not as bad as in 2023, but there are instances when there's not enough staff on hand.
• Volume and transfer bags. Short connecting bags are (normally) given preference for offload as they are a product that needs to be protected. So, usually, the first train of baggage bins to leave the aircraft heads for a transfer input point.

Well, the journey between a shorthaul gate and the belts in T2 is less than 500 metres long, I'd be very surprised if it didn't.

For longhaul: In short it's because the logistics crews offloading bags don't follow the procedure and it seems that their management isn't interested in managing them.

Say that you're flying ORD-LHR. Normally, what the team in ORD will do is this: they will fill some 10/15 bins with bags. These bins will be 'segregated'. Two/three will contain short connecting bags, a couple more will have long connecting bags, then you have the London terminating ones: premium and non-premium. These are then loaded into the aircraft according to the LIR, the Loading Instruction Report. Basically it's a drawing with all the positions in the hold and each bin type marked. Normally cargo comes in first, then non-premium, then long connecting, then premium, then short connecting.

At other airport, the crew handling the arrival are allocated the bins by their supervisor. So you'll be at aircraft side and your supervisor will say: "Tom you take the short connex, Dick you take the priority, Harry you get the long connex" and so on. At LHR the crews are allocated the bins by number, so they'll wait for that specific bin. Which is mental. Then they'll drive to wherever they need to, and simply offload the first bin they have on their train. They could have two priority bins and one economy bin; if the last one is closest, they'll offload that. Not everyone does it, but most do. And this is because historically no one have been managing them properly. Looking at the data, there is a tendency to have priority bags amongst the first off the belt, but it's not a certainty.

Crew bags are normally in the priority bin, and having seen the data I'd say that they're sometimes on top, but not quite always.

On shorthaul, there is no segregation between premium and non-premium. The only segregation into London is between London terminating and connecting bags. This is because your average 156-seater A320 will have between 80 and 100 bags onboard, with a 60-40 split between arriving and terminating. If you were to create a Premium bin, you'll be carrying an extra container that will be half empty, and the tare of a shorthaul ULD is in the region of 70kg. A while back the Data team did an analysis and segregating premium bags on shorthaul would cost tens of millions in extra fuel per year.