The Doctor has encountered ships with residents of Earth who were sent away to avoid/survive some sort of disaster on a number of occasions. I haven't seen the episode in question yet, so it's possible that he's explicitly referring to other ships escaping from the same situation, or to ships of Earth evacuees in general.
I think the earliest recorded encounter with a similar ship (residents of Earth evacuated to avoid/survive some sort of disaster), was The Ark (Original series 3, story 6; the First Doctor, Steve, and Dodo).
The next similar example is the already-mentioned The Ark In Space (Original series 12, story 2; the Fourth Doctor, Sarah Jane, and Harry). However, the Nerva space station was actually still in our solar system (I want to say it was in orbit around Earth, but I can't recall for certain, or find a comment to back that up; however, they're using transmit technology to get to Earth at the end of the story, and every time we've seen that technology in the past (like The Seeds of Death) it's being used for in-system transportation, not interstellar).
Then there's Frontios (Original series 21, story 3; Fifth Doctor, Tegan, Turlough); that's not a ship, but a "distant planet where some of the last vestiges of humanity are struggling to survive" (from the Wikipedia entry.
In the revived series, along similar lines, we have:
- New Earth (New series 2, story 1; Tenth Doctor and Rose; planet where humanity resettled after the Earth was destroyed in the distant future);
- Utopia (New series 3, story 11; Tenth Doctor, Martha, and Captain Jack; last remnants of humanity are trying to get to a place called Utopia; no spaceship involved);
- The Beast Below (New series 5, story 2; Eleventh Doctor and Amy; spaceship holding UK evacuees avoiding the death of Earth's sun [presumably from the same event as New Earth]);
- Dinosaurs on a Spaceship (New Series 7, story 2; Eleventh Doctor, Amy and Rory; spaceship used as a space ark by Earth's older "ruling" species, the Silurians; form the Doctor's perspective, it might fit perfectly in with these others).