Hi Peyton.
On "Upstairs Downstairs", it was the family matriarch, Lady Marjorie Bellamy, who was on the Titanic.
The late Rachel Gurney, who played Lady Marjorie, had decided to leave the series. The producers thus had her traveling to New York, to visit her and Richard's daughter Elzabeth.
On the series, at the end of one episode, the butler, Mr. Hudson says to Lady Marjorie "Have a Nice Trip, My Lady", and we see him waving as the family car drives off.
In the last scene, Richard is dictating a cable to be sent to her, as he recites "To Lady Marjorie Bellamy, Cabin #..., RMS Titanic", as we see a desktop picture of Lady Marjorie.
The next episode begins with the family having been notified of the tragedy. Lady Marjorie is declared missing, along with her maid, Mrs. Roberts. However, Mrs. Roberts returned home, and told them how, during the loading of the lifeboats, Lady Marjorie went off to help a young girl find her mother, while Mrs. Roberts was placed in a lifeboat, where she watched the ship sink as she cried out "We've got to go back for My Lady"!!
A reference to the sinking was made during the second-to-last episode of the Series' final season.
In that one, James, who had just returned from New York, shared his thoughts about his trip with his cousin, Georgina, whose mother also died on the Titanic.
James mentioned how, when his ship passed near the area of the sinking, he found himself looking out at the water, and "knowing she was down there".