RMS Titanic
For the ship in Voyage of the Damned, see Titanic (spaceship).
I never cared for the word "impregnable". Sounds too much like "unsinkable". What's wrong with "unsinkable"? Oh, nothing', said the iceberg to the Titanic.
The RMS Titanic was a luxury ocean liner on Earth in the early 20th century noted as being the largest ship of its time. It is known famously for having been called "unsinkable", yet sinking on it's maiden voyage in 1912.
The Doctor, Ace and Bernice Summerfield travelled to the Titanic tracking Huitzilin and were on the ship when it collided with the iceberg. (NA: The Left-Handed Hummingbird) El Ape, a temporary traveling companion of the Doctor, actually caused the ship to sink (DWM: Follow That TARDIS!)
An issue of the The Daily Mirror describing the disaster travelled to Gallifrey, where it was read by Borusa. Upon noticing this, the Doctor noted that he had nothing to do with the ship's destruction. (DW: The Invasion of Time)
Later the Doctor persuaded several people to not board the liner prior to its maiden voyage. (DW: Rose). The Doctor told Jabe Ceth Ceth Jafe that he had once been on a ship that "they said [...] was unsinkable. I ended up clinging to an iceberg. It wasn't half cold." This seems a probable reference to his adventure on the Titanic. (DW: The End of the World).
Recreation
Max Capricorn, the head of Max Capricorn Cruiseliners, constructed a starship replica of the Titanic for a voyage from Sto to Earth for the observation of "primitive cultures" on Christmas Day, 2008. (DW: Voyage of the Damned). This Titanic was named after "the most famous ship on Earth" by Max Capricorn himself, likely because he knew it was to be crashed later.
It may be that the Doctor was wearing the same tuxedo on the starship Titanic as he wore on the seaship Titanic, as hinted at by the line: "Bad name for a ship. Either that or this suit is really unlucky." (DW: Voyage of the Damned)