In which year did Great Britain get its first Prime Minister?

The accepted date is 1721, when Robert Walpole became Prime Minister.

The position of Prime Minister was not created; it has evolved slowly and erratically over three hundred years. Its origins are found in constitutional changes that occurred during the Revolutionary Settlement (1688-1720) and the resulting shift of political power from the Sovereign to Parliament. Early Prime Ministers (1720-1784) were at best ambivalent about that description; many refused to acknowledge or use the title. The position was given little formal recognition and was not mentioned in legal documents. Between 1784 and 1911, numerous accidents of history and political developments led to unofficial but popular acceptance of the office. By the 1830s, the Prime Minister became "first among equals" in the Cabinet and Head of Her Majesty's Government. By the turn of the 20th century, the modern Premiership had emerged; it had become the preeminent position in the constitutional hierarchy vis-a-vis the Sovereign, Parliament and Cabinet. Early in the century, legislation marginalized the influence of the House of Lords in the law-making process and indirectly enhanced the Prime Minister's power, giving rise to concerns that the office had become too "presidential". Later, however, several acts and political changes placed some limits on the Premier's authority. (Source wikipedia)