The mystery ship does indeed appear to be the Normannia, as Alain Hobbs has concluded. The article below on Dover Ferry Photos states that the engine room was flooded, seriously damaging the turbine machinery. It also includes a photograph of her high and dry at low tide at the shallow end of the Admiralty Pier where she had been moved in order to install a concrete box to render her watertight until permanent repairs could be effected. Derek Donnelly commented on the photo on Facebook as follows: "She is laying behind "A" shed where the Packet yard put a temporary concrete repair in the gash in her side. As Alain said she hit the submerged girder-work of the old paddle steamer berth at no 5 berth Ad pier where she was going to lay by for crew change. She moved ,with all pumps going, to here so she would sit on the bottom at low tide."
http://www.doverferryphotosforums.co.uk/ts-normannia-past-and-present/
There was certainly one ferry which sank in Dover in peacetime and that was the Belgian ferry Ville de Liege back in 1929. She grounded on the Mole Rocks, which are now buried beneath the Hoverport, and was holed and settled on the bottom. The Mole Rocks were the remains of the abortive attempt by Henry VIII to build a great mole out into the sea and presented a danger to shipping for centuries thereafter. The Ville de Liege was subsequently completely rebuilt into Belgium's first car ferry and renamed the London-Istanbul.