Prime Minister is a title given to heads of government in several states.
On Earth, the United Kingdom was headed by a Prime Minster. The Doctor had numerous encounters with various British Prime Ministers, most notably Winston Churchill, who encountered several of his incarnations, (TV: Victory of the Daleks) Harriet Jones, who was deposed by him, (TV: The Christmas Invasion) and Harold Saxon, which was an alias used by the Master. (TV: The Sound of Drums/Last of the Time Lords)
The Indian government was also headed by a Prime Minister. In 1984, the position was held by Indira Gandhi. As she told the Egyptian Pharaoh Erimem, Peri Brown considered her to be an effective female leader in contrast to her British counterpart and contemporary Margaret Thatcher. Given that Erimem was from the 14th century BC, she had unsurprisingly never heard of either Gandhi or Thatcher. (AUDIO: The Eye of the Scorpion)