Vivien Rook noted that Lucy Saxon, being the wife of Prime Minister Harold Saxon, was Britain's First Lady. (TV: The Sound of Drums)
At Kerb!am, the Thirteenth Doctor used psychic paper to make Judy Maddox believe that she and Team TARDIS were relatives of the First Lady. When Judy found that the Doctor had a binary vascular system, the Doctor claimed it to be courtesy of the First Lady. (TV: Kerblam!)