The Kremlin was the headquarters for the government of the Soviet Union.
Turlough was told by the Fifth Doctor that he was not welcome in the Kremlin. (AUDIO: Singularity) This could have been because of his visit to the Kremlin centuries earlier. (AUDIO: Thin Ice)
The brothers Yevgeni and Yasha Lemayev worked at the Kremlin. (AUDIO: Thin Ice)