It tells the story of a murder on a vessel carrying nuclear missiles, following a police officer played by Suranne Jones as she boards the boat to investigate.
The first episode has her character, Detective Chief Inspector Amy Silva of the “Scottish Police Service”, flown out to the submarine by helicopter as it continues its patrol at sea.
She is tasked with carrying out interviews and forensic investigations alone, while her efforts are frustrated by suspicious crew members with mysterious motives.
A naval source told The Independent that if there was a murder on a submarine, the investigation would happen rather differently.
In the scenario shown in Vigil, in which the boat is on patrol, an initial investigation would instead be carried out on board.
A small group of officers on each submarine is trained to deal with serious crimes and a dedicated compartment has devices to take photos and other evidence.
If someone was killed, the area would be treated as a crime scene and detailed photos would be taken in order for a reconstruction to be created if necessary, the source said.
All the officers involved would normally be on other duties because, the source said, there cannot be “one person permanently doing nothing in case someone dies”.
Initial statements would be taken from the crew and those documents and all other evidence would be handed over to a civilian police force on the submarine’s return.
The naval source said that in an extreme circumstance, a commander couldcutshort a patrol but in the case of a Trident submarine it was more likely that the journey would be finished as planned.
“At that point, the information would be handed to a regional police force that would do the investigation with whatever support the Navy provides for them,” he added.
“The Navy would be falling over backwards to find out what went wrong.”
The response on board would be led by a “senior rating”, or coxswain, and then a commanding officer would make a decision on where to put the body.
In Vigil, the victim, Craig Burke, played by Martin Compston, is stored in a torpedo tube because – as another character explains – it would be cooled by the sea water.
The naval source said that in reality, a body would probably be left in the submarine’s main fridge, after food stocks were removed.
He said a torpedo tube would work for a short time but that Mediterranean water would certainly be too warm to preserve a body for examination.
Asked whether there were any circumstances where a civilian police officer would be taken out to a submarine on patrol, the source said local police could board a boat that was moored or at its home base or on exercises.
But he thought it unlikely during an active patrol given safety concerns and training in progress, as well as the fact that food and oxygen are carefully calculated according to crew numbers.
Vigil airs on Sundays at 9pm on BBC One.