At LHR we used to, and I presume still do, have about 3 a month arrive dead.
Depending on if there is a doctor on board, they could have been prounounced as life being extinct, or common sense could have prevailed, and someone who was obviously dead was left alone and treated in as dignified way as possible.
The proccedure, irrespective was to have Port Health's doctor certify death on arrival. And after a quick look to make sure there were no suspcious circumstances, the Coranors Officer would arrange for the body to be removed to a morgue.
I must have dealt with 7 or 8 sudden deaths in my time at LHR, the bodies were stored in different places, from being strapped laying on a row of seats, to sat strapped in and covered over. One was placed in the galley on the top deck of a 747, which was a bit awkward when it came to removal of the body down the spiral staircase, rigour mortice having set in!
As far as the UK were concerned, if the cause of death was obvious, the coranor would authorise the repatriation of a forgien national and hold a 'paper' inquest. If the body was that of a UK National, or the cause of death was unknown, then the usual inquest would follow.
I went to a call to a sudden death on a Swiss aircraft once, which was waiting to depart, having got to the air bridge, I found the body wrapped in a sheet laying on the floor, and the aircraft pushing back, and no one else about!.....The crew were not amussed when they were told to get back on stand by ATC, and they were going no where until I had investigated things!