By the late eighteenth-century, the Court had developed an electoral machine that ensured that there was a permanent party in the House of Commons that obeyed the King's wishes (sometimes called 'the King's men' or 'King's friends'). More often than not, George III could choose a Prime Minister to his liking and could influence parliamentary votes e.g. the India Bill of 1783.
However the Reform Act 1832 swept this away and thereafter almost every MP was now either a Liberal or Conservative. Parties were now more dependent on general elections to win power rather than Crown patronage. They looked more to appealing to the increased electorate for power than the monarch. They became more coherent, organised parties. The power of the monarch to choose his/her own ministers was seriously curtailed.
The power of Queen Victoria (1837-1901) was considerably weaker compared to George IV (1820-1830). Victoria often had to accept Prime Ministers who, if she had the choice, she would never have appointed e.g. Palmerston and Gladstone.
As the British constitution is uncodified, its development is evolutionary and so it is harder to pinpoint an exact date, unlike for example France, where its many revolutions and written constitutions make it easier to determine the powers of public offices.
Source: J. C. D. Clark, English Society 1688-1832. Ideology, Social Structure and Political Practice during the Ancien Regime (Cambridge: Cambridge University Press, 1985).