A Royal Navy submarine missing since it was sunk by a Nazi ship 76 years ago has been discovered 40 metres beneath the waves off the coast of Denmark.

HMS Tarpon was destroyed by a heavily armed German merchant vessel with the loss of at least 50 British lives on 10 April 1940. The wreck, which was reached by Danish divers 50 miles from the shore last week, is being treated as a war grave.

The divers found some of the hatches open, the glass in the periscope shattered and severe destruction below the tower where it appeared to have been hit by a depth charge. There was also evidence of a battle, with two of its torpedo tubes empty. German naval records suggest the Tarpon had fired twice at a German merchant ship before being sunk in a devastating counterattack.

The submarine was discovered in March by a Danish war museum owner, Gert Normann Andersen, and a UK marine archaeologist, Dr Innes McCartney, who were seeking wrecks from the first world war Battle of Jutland. It means families of the seamen finally know exactly where their loved ones perished during the second world war. A Danish TV station, DR3, broadcast live footage of the vessel last week, bringing pictures of the wreck to the world for the first time.

“It never crossed my mind that it would be found,” said Sheila Summer, 77, from Crosby in Merseyside, who was 11 months old when her father, Reginald Kellond, an engine room artificer on the Tarpon, died aged 31. “It was thought-provoking to see the wreck on the bottom and to know my father had been in there.”

Just before the submarine set sail, the engineer had sent his wife a last letter.

“I am very glad to hear that Sheila is much better,” he wrote. “I believe that whooping cough is a sensible thing to watch in its early stages. I can guess that you are fairly fed-up and tired and I am very sorry that it is impossible for you to come here … by the time you get this we shall be at sea … well pet, this is all for now. Cheerio and all the best, love Reg xxxxx.”

He was never heard from again.

The 84-metre T-class submarine sailed from Rosyth, Fife, in order, it is thought, to attack German merchant ships supplying arms to Nazi-occupied Norway. German records suggest that five days after setting out, it fired two torpedos at Schiff 40, an armed merchant ship, both of which missed. The German ship detected the Tarpon using sonar, saw its periscope and dropped depth charges, sinking it within a few hours.

“No one even knew it was there,” said McCartney, a veteran submarine finder, who was on board the explorer ship last week when divers filmed the wreck. “It looked very bad. They had depth charged it on several occasions. The damage was so severe behind the conning tower it would have flooded in seconds.”

There was also a crater on the seabed, a rare phenomenon apparently created by one of the powerful depth charges.

McCartney said the submarine stood almost upright on the seabed and had attracted shoals of cod as well as ocean debris including ropes and fishing nets, some of which had to be cleared before filming.

He said 57 British submarines were lost in the second world war and two more were found recently – the HMS P311, another T-class, off the coast of Italy, and the S-class HMS Simoom off Turkey.

“The question for the Ministry of Defence is how to protect them from threats including fishing trawlers and illegal metal reclaimers,” McCartney said. “After all, they are the tombs of British sailors.”