A list of PMs for my TL so far.
In The Name of the King!
1766: William Pitt, 1st Earl of Chatham (Whig) [1]
1767: Charles Watson-Wentworth, 2nd Marquess of Rockingham (Whig) [2]
1774: Charles Watson-Wentworth, 2nd Marquess of Rockingham (Whig) [3]
1781: Charles Watson-Wentworth, 2nd Marquess of Rockingham (Rockinghamite Whig) [4]
1788: Frederick North, 2nd Earl of Guildford ('Tory') [5]
1791: John Montagu, 5th Earl of Sandwich (Northite Tory-Pittite Tory Coalition) [6]
1795: William Pitt 'The Younger' (Pittite Tory-Burkite Whig Coalition) [7]
1800: William Pitt 'The Younger' (Pittite Tory-Burkite Whig Coalition) [8]
1806: Sir Alexander Hamilton, 1st Baronet (Pittite Tory-Old Whig Coalition) [9]
1810: Sir Alexander Hamilton, 1st Baronet (Reform Whig-Tory Coalition) [10]
1816: Sir Alexander Hamilton, 1st Baronet (Reform Whig) [11]
[1] The man who had engineered Britain's expansion into being a world spanning empire and the Europe's premier naval power was unfortunately struck down by disease and forced to retire. His rather lameduck one year administration ended, and the King casting around for alternatives, called a general election
[2] The Marquess of Rockingham emerged as leader of the largest faction of Whigs, and was able to rally them behind him. The King was forced to put up with a man he didn't particularly like. If he'd known the longevity of Rockingham's career, he might have resisted more.
[3] While his first term was mostly occupied with securing Britain's gains by attempting to build diplomatic bonds across the country, in his second term, Rockingham became decidedly more radical. A compromise was reached with the American colonies wherein they became direct parts of the Kingdom of Great Britain. During his second term, the coalition of Whigs he had built began to collapse, but he managed to maintain a majority by appealing to both Radical and Tory sentiments.
[4] In his final term, Rockingham's strident position was considerably weakened by the division of British politics into four stable parties. His faction of Whigs managed to cling on to power, narrowly. Rockingham began to suffer internal problems as Radicals became more important, and came to rely on the stable 'American Whig' faction.
[5] An aged Lord North finally attained the premiership, forging a coalition of Tories and conservative Whigs. North never claimed to be a Tory, but his government would become Tory after the fact. He mostly attained government due to dissatisfaction with the increasing radicalism of the Rockinghamites and exhaustion with Rockingham's domination of government for the last two decades.
[6] North's death in government led to the son of one of his close allies gaining his seat. North's death broke the weak coalition of 'Tories', into parts that followed his more traditionalist path and the reformers under Pitt. Sandwich was able to just about maintain a shaky coalition, but the pressures of the Revolutionary Wars, led to a deterioration which finally collapsed when France under Jacques Hebert managed to crush invaders and insurrection, posing a direct threat to the rest of Europe.
[7] William Pitt led his faction of reforming Tories into government, requiring the support of Edmund Burke's faction of Whigs to prop him up. The Rockinghamites had come under the rule of Charles James Fox, and had transformed into the Radical Whigs and had become relatively marginalised due to the Revolutionary Wars.
[8] Pitt continued policies of trying to repair Britain's massive national debt, expanding her navy, financially supporting members of the Coalition against France, and propping up governments-in-exile in the colonies. The 'American Whig' faction was by now thoroughly riven, usually between either the Pittites or the Radical Whigs. Pitt was however weakened by the expansionist policy that France had taken under Sieyes. Burke's death had also left Pitt in a difficult position as the Burkites argued over his legacy.
[9] The energetic (and controversial) New Yorker triumphed over other challengers after Pitt died in office. He was very much in Pitt's mould, a financial and political reformer, and aggressive supporter of commerce and the Empire. He continued the alliance with the Burkites, now coalesced under the Duke of Portland, to keep out the growing Radicals. Hamilton benefitted from the humiliation of France in the field with the close of hostilities in 1806.
[10] The colossal victories of France by 1810, led to calls from the Old Whigs as well as rejuvenated Radical Whigs, to come to some sort of permanent settlement with the French government, pointing out how the Terror had been abandoned within France since Sieyes had displaced Hebert. Hamilton was determined to finish what he had started, and formed an alliance with the Tories. He reconstituted the Pittites as Reform Whigs, differentiating them from Whig traditionalism and Whig radicalism alike.
[11] The final victory of the Coalition over the Republican French, restoring the monarchy at least led to an overwhelming wave of patriotic fervour which delivered Hamilton back into power with a landslide majority, allowing him to abandon partners in power.