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Answer
Commonly regarded as the first British Prime Minister
Robert Walpole
Oversaw the founding of the NHS
Clement Attlee
Was a woman (name any of them)
Margaret Thatcher; Theresa May; Liz Truss
Was assassinated
Spencer Perceval
The first Labour Prime Minister
Ramsay MacDonald
The most recent Liberal (or Liberal Democrat) Prime Minister
David Lloyd George
Founded the Metropolitan Police Service
Robert Peel
Wrote and published sixteen novels, one of which was subtitled "a moral tale, though gay"
Benjamin Disraeli
Held all four Great Offices of State (PM, Chancellor, Home Secretary, and Foreign Secretary)
James Callaghan
Was despised by the suffragette movement for his refusal to grant women the vote, causing them to try to burn down a theatre he was in and throw an axe at his head on the same day
H. H. Asquith
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Answer
Led a "caretaker ministry" for a month whilst waiting for the next Prime Minister to return from holiday in Italy
Duke of Wellington
Was born outside of the British Isles (name either of them)
Andrew Bonar Law; Boris Johnson
The most recent Prime Minister who was born in Edinburgh
Tony Blair
The most recent Prime Minister who didn't go to university
John Major
The most recent person to have been Prime Minister whilst (briefly) being a member of the House of Lords
Alec Douglas-Home
The only 20th-century Conservative leader, apart from William Hague, who was never Prime Minister (first name and last name required)
Austen Chamberlain
Was the Earl of a port city in northern England
Earl of Liverpool
The namesake of a contentious UK government declaration relating to Israel and Palestine
Arthur Balfour
The namesake of a convention that says the House of Lords shall not try to prevent any legislation that was promised in the government's election manifesto
Lord Salisbury
Led what is sometimes known as the "Who? Who?" ministry
b) it's bizarre that some questions are 'name any of them', where some are only 'the most recent' - could these be made more consistent?
nonetheless this is a great quiz!