I thought about Lloyds and whether "the merchants" had been paid out. Alternatively as this was a warship whatever it was carrying may not have insured.

There is absolutely no doubt who owns the ship - the owners at the time the vessel sank.

One example I,ve been involved with was the case of HMS Edinburgh, a cruiser that was sunk on its way back from Russia carrying gold bullion belonging to the Soviet Government. The gold was in payment for supplies being sent to Russia. The ship belonged to and still belongs to HM Government, the gold once recovered was shared between the Soviet Government, the British Government and the salvage company.

Additionally warships are automatically designated war graves.