So lets get this right.......total chaos at LHR because HAL can't keep the runways open or provide proper remote de-icing facilities like most other places in Western Europe. Tens of thousands of passengers disrupted, probably upwards of 50000 bags being stacked up everywhere and anywhere there's space, all the baggage handling equipment out of position because the schedules gone to cock and at 2am you expect an army of BA staff to magically appear from somewhere? Well pardon my cynicism but where exactly do you expect these staff to come from? There's no night shift for these staff, we can't get any more into LHR because (as you obviously haven't noticed) half the bleedin roads in the South East are closed and the staff who'd extended their shifts for so long already are busy trying to find gates and handling for the numerous aircraft still stuck off stand, and booking hotels and transfers for the thousands of stranded passengers (of course you wouldn't appreciate that practically every hotel in the LHR area was filling up very nicely by 12 noon).
Then of course 10000 people arrive today wanting their bags back, leading to enormous queues and a total swamping of the phone system. The bags are almost certainly sitting around in an pallet somewhere in the T4 area, but all the pallets are throughly covered in snow, which means it takes ten times as long to locate and identify each one and ten times as long to move it from A to B, but we don't have access to ten times as many staff to deal with that, so its an unfortunate fact of life that people are going to have to wait. Unpleasant, but unavoidable.
To suggest that passengers have just been abandoned is, frankly, stretching credulity. Abandoned is when you get off the aircraft, are told that you've got to arrange your own hotel and transport at your own expense, told you may get your bags back or not, but it will be sometime in the next two weeks and when you turn up the next day there's nobody to speak to, not even an overwhelmed Customer Services desk.
The whole situation is lamentable, but theres only so much you can do with a finite number of staff when your operation is virtually shut down due to the inability of the airport operator to keep their show on the road.