It occurs to me that threads like this would be helped by the creation of a template OTL list of leaders that could then be edited, and would provide a guide to people who may not know about a country's political background. So to start off, here's the OTL list of British Prime Ministers.
Prime Ministers of Great Britain
1721-1742: Sir Robert Walpole (Whig)
1742-1743: Spencer Compton, 1st Earl of Wilmington† (Whig) [1]
1743-1754: Henry Pelham (Whig)
1754-1756: Thomas Pelham-Holles, 1st Duke of Newcastle (Whig)
1756-1757: William Cavendish, 4th Duke of Devonshire (Whig)
1757-1762: Thomas Pelham-Holles, 1st Duke of Newcastle (Whig) [2]
1762-1763: John Stuart, 3rd Earl of Bute (Tory)
1763-1765: George Grenville (Grenvillite Whig)
1765-1766: Charles Watson-Wentworth, 2nd Marquess of Rockingham (Rockinghamite Whig)
1766-1768: William Pitt the Elder, 1st Earl of Chatham (Chathamite Whig)
1768-1770: Augustus FitzRoy, 3rd Duke of Grafton (Chathamite Whig)
1770-1782: Frederick North, Lord North (Tory) [3]
1782-1782: Charles Watson-Wentworth, 2nd Marquess of Rockingham† (Rockinghamite Whig)
1782-1783: William Petty-FitzMaurice, 2nd Earl of Shelburne (Chathamite Whig)
1783-1783: William Cavendish-Bentinck, 3rd Duke of Portland (Whig leading Whig-Tory Coalition)
1783-1801: William Pitt the Younger (Pittite Tory) [4]
Prime Ministers of the United Kingdom of Great Britain and Ireland
1801-1801: William Pitt the Younger (Pittite Tory)
1801-1804: Henry Addington (Pittite Tory)
1804-1806: William Pitt the Younger† (Pittite Tory)
1806-1807: William Wyndham Grenville, 1st Lord Grenville (Whig leading Whig-Tory-Independent Coalition) [5]
1807-1809: William Cavendish-Bentinck, 3rd Duke of Portland (Tory) [6]
1809-1812: Spencer Perceval† (Tory) [7]
1812-1827: Robert Banks Jenkinson, 2nd Earl of Liverpool (Tory)
1827-1827: George Canning† (Canningite Tory leading Canningite Tory-Whig Coalition)
1827-1828: Frederick John Robinson, 1st Viscount Goderich (Canningite Tory leading Canningite Tory-Whig Coalition)
1828-1830: Arthur Wellesley, 1st Duke of Wellington (High Tory)
1830-1834: Charles Grey, 2nd Earl Grey (Whig)
1834-1834: William Lamb, 2nd Viscount Melbourne (Whig)
1834-1834: Arthur Wellesley, 1st Duke of Wellington (High Tory as caretaker leader of provisional Conservative government)
1834-1835: Sir Robert Peel (Conservative minority)
1835-1841: William Lamb, 2nd Viscount Melbourne (Whig)
1841-1846: Sir Robert Peel (Conservative)
1846-1852: Lord John Russell (Whig minority) [8]
1852-1852: Edward Smith-Stanley, 14th Earl of Derby (Protectionist Conservative minority)
1852-1855: George Hamilton-Gordon, 4th Earl of Aberdeen (Peelite Conservative leading Peelite Conservative-Whig Coalition)
1855-1857: Henry John Temple, 3rd Viscount Palmerston (Whig minority)
1857-1858: Henry John Temple, 3rd Viscount Palmerston (Whig)
1858-1859: Edward Smith-Stanley, 14th Earl of Derby (Conservative minority) [9]
1859-1865: Henry John Temple, 3rd Viscount Palmerston† (Liberal)
1865-1866: Lord John Russell, 1st Earl Russell (Liberal)
1866-1868: Edward Smith-Stanley, 14th Earl of Derby (Conservative minority)
1868-1868: Benjamin Disraeli (Conservative minority)
1868-1874: William Ewart Gladstone (Liberal)
1874-1880: Benjamin Disraeli (Conservative)
1880-1885: William Ewart Gladstone (Liberal)
1885-1886: Robert Gascoyne-Cecil, 3rd Marquess of Salisbury (Conservative minority) [10]
1885-1886: William Ewart Gladstone (Liberal minority with Irish Parliamentary Party support)
1886-1892: Robert Gascoyne-Cecil, 3rd Marquess of Salisbury (Conservative)
1892-1894: William Ewart Gladstone (Liberal minority with Irish Parliamentary Party support)
1894-1895: Archibald Primrose, 5th Earl of Rosebery (Liberal minority)
1895-1902: Robert Gascoyne-Cecil, 3rd Marquess of Salisbury (Conservative leading Conservative-Liberal Unionist Coalition)
1902-1905: Arthur Balfour (Conservative leading Conservative-Liberal Unionist Coalition)
1905-1906: Sir Henry Campbell-Bannerman (Liberal minority)
1906-1908: Sir Henry Campbell-Bannerman (Liberal)
1908-1910: Herbert Henry Asquith (Liberal)
1910-1915: Herbert Henry Asquith (Liberal minority with Irish Parliamentary Party support)
1915-1916: Herbert Henry Asquith (Liberal leading Liberal-Conservative National Government
1916-1922: David Lloyd George (Liberal leading Liberal-Conservative-Labour National Government [11]
1922-1922: Andrew Bonar Law (Conservative) [12]
Prime Ministers of the United Kingdom of Great Britain and Northern Ireland (de facto until recognised by law 1927)
1922-1923: Andrew Bonar Law (Conservative) [12]
1923-1923: Stanley Baldwin (Conservative)
1923-1924: Stanley Baldwin (Conservative minority)
1924-1924: Ramsay MacDonald (Labour minority)
1924-1929: Stanley Baldwin (Conservative)
1929-1931: Ramsay MacDonald (Labour minority)
1931-1932: Ramsay MacDonald (National Labour leading National Labour-Conservative-Liberal National-Liberal National Government)
1932-1935: Ramsay MacDonald (National Labour leading National Labour-Conservative-Liberal National National Government)
1935-1937: Stanley Baldwin (Conservative leading Conservative-Liberal National-National Labour National Government
1935-1940: Neville Chamberlain (Conservative leading Conservative-Liberal National-National Labour National Government
1940-1945: Winston Churchill (Conservative leading Conservative-Liberal National-Labour National Government
1945-1945: Winston Churchill (Conservative leading Conservative-Liberal National National Government
1945-1951: Clement Attlee (Labour)
1951-1955: Winston Churchill (Conservative including National Liberal)
1955-1957: Sir Anthony Eden (Conservative including National Liberal)
1957-1963: Harold Macmillan (Conservative including National Liberal)
1963-1964: Sir Alec Douglas-Home (Conservative including National Liberal)
1964-1970: Harold Wilson (Labour) [13]
1970-1974: Edward Heath (Conservative) [14]
1974-1976: Harold Wilson (Labour/Labour minority) [15]
1976-1979: James Callaghan (Labour minority with Liberal and Ulster Unionist Party support) [16]
1979-1990: Margaret Thatcher (Conservative) [17]
1990-1996: John Major (Conservative) [18]
1996-1997: John Major (Conservative minority with Ulster Unionist Party support)
1997-2007: Tony Blair (Labour)
2007-2010: Gordon Brown (Labour)
2010-present: David Cameron (Conservative leading Conservative-Liberal Democrat Coalition)
[1] First PM to die in office.
[2] First PM to serve for two separate terms.
[3] Resigned after the first vote of no confidence in history
[4] Dubbed a Tory by his detractors, but considered himself a reform Whig. His supporters only retroactively accepted the label Tory and had little to no connection with the previous Tory Party.
[5] The so-called "Ministry of All the Talents".
[6] Generally counted as a Tory, he was a figurehead to a Tory government, although earlier he had headed a Whig one, also as a figurehead.
[7] Only PM to be assassinated.
[8] Minority government possible due to split in Conservatives between Protectionists and Peelites.
[9] During Derby's period in government, the opposition Peelite Conservatives and Whigs merged to form the Liberal Party.
[10] The 1885 election produced a hung parliament with the Irish Parliamentary Party holding the balance. The Conservatives were actually the smaller of the two major parties, hence the government's rapid collapse.
[11] Only PM to have a language other than English (Welsh) as his mother tongue.
[12] Only PM to be born outside the British Isles (in Canada).
[13] During Wilson's term in power, in 1968, the National Liberal Party formally merged into the Conservatives (which had been de facto the case for many years).
[14] After the first election of 1974 produced a hung parliament, Heath attempted to form a coalition deal with the Liberals, but failed and left Labour to form a minority government alone.
[15] Labour had only a tiny majority, and by-elections had demolished it by the time he stood down as PM.
[16] The pacts with the Liberals and UUP were temporary, and the government was eventually defeated by a vote of no confidence.
[17] First (and thus far only) female PM. During her time in power, the right wing of the Labour Party broke away to form the Social Democratic Party, allying itself with the Liberals to form the SDP-Liberal Alliance. In 1988 the two formally merged to form the Social and Liberal Democrats, later abbreviated to Liberal Democrats.
[18] Again, Major had a small majority after 1992 and this was eaten away by by-elections, being reduced to zero at the end of 1996.