Question: What party was both, Harold Macmillan and Keith Joseph apart of?

Context articles: The Middle Way (Harold Macmillan book)
Conservative government, 1957–1964
Daniel Macmillan, Viscount Macmillan of Ovenden
Alexander Macmillan, 2nd Earl of Stockton
Harold Macmillan
Keith Joseph
Maurice Macmillan
Federation of Conservative Students
United Kingdom general election, 1959
Profumo affair

The Middle Way is a book on political philosophy written by Harold Macmillan (British Conservative Party politician and later prime minister of the United Kingdom).
 It was first published in 1938 (by Macmillan & Co, Ltd, London).
 It advocated a broadly centrist approach to the domestic and international problems of that time, and was written during a period when Macmillan was out of active office.
 He called for a programme of nationalisation at least as ambitious as then advocated by the Labour Party (UK).
The Conservative government of the United Kingdom that began in 1957 and ended in 1964 consisted of three ministries: the first Macmillan ministry, second Macmillan ministry, and then the Douglas-Home ministry.
 They were led by Harold Macmillan and Sir Alec Douglas-Home, who were appointed respectively by Queen Elizabeth II.
Daniel Maurice Alan Macmillan, Viscount Macmillan of Ovenden (born 9 October 1974) is a British fashion designer and the only son of Alexander Macmillan, 2nd Earl of Stockton.
 As the heir apparent to an earldom, he uses his father's secondary title of Viscount Macmillan of Ovenden as a courtesy title.
 He is a great-grandson of the former Prime Minister Harold Macmillan, 1st Earl of Stockton.
Alexander Daniel Alan Macmillan, 2nd Earl of Stockton (born 10 October 1943) is a Conservative Party politician in the United Kingdom.
 He is the first son of the late Conservative politician Maurice Macmillan and the first grandson of former prime minister Harold Macmillan.
Maurice Harold Macmillan, 1st Earl of Stockton, {'1': ", '2': ", '3': ", '4': "} (10 February 1894 – 29 December 1986) was a British statesman of the Conservative Party who served as Prime Minister of the United Kingdom from 1957 to 1963.
 Nicknamed "Supermac", he was known for his pragmatism, wit and unflappability.
Keith Sinjohn Joseph, Baron Joseph, (17 January 1918 – 10 December 1994), known as Sir Keith Joseph, 2nd Baronet, for most of his political life, was a British barrister and politician.
 A member of the Conservative Party, he served in the Cabinet under four prime ministers: Harold Macmillan, Sir Alec Douglas-Home, Edward Heath and Margaret Thatcher.
 He was a key influence in the creation of what came to be known as "Thatcherism" and the subsequent decline of one-nation conservatism and the postwar consensus.
Maurice Victor Macmillan, Viscount Macmillan of Ovenden PC (27 January 1921 – 10 March 1984) was a British Conservative Party politician and Member of Parliament.
 He was the only son of Harold Macmillan, who previously served as Prime Minister of the United Kingdom.
The Federation of Conservative Students (FCS) was the student organisation of the British Conservative Party from the late 1940s to 1986.
 It was created to act as a bridge between the student movement and the Conservative Party.
 In its final years it became known colloquially as "Maggie's Militant Tendency", in reference to then Prime Minister Margaret Thatcher and to Militant, an entryist group active in the Labour Party at the time.
 The FCS was then broken up by the Chairman of the Conservative Party, Norman Tebbit, after one of its members had accused previous former Prime Minister Harold Macmillan of war crimes in extraditing Cossacks to the Soviet Union.
 The FCS was replaced by the Conservative Collegiate Forum.
This United Kingdom general election was held on 8 October 1959.
 It marked a third consecutive victory for the ruling Conservative Party, now led by Harold Macmillan.
 The Conservatives increased their overall majority again, to 101 seats over the Labour Party led by Hugh Gaitskell and the Liberal Party led by Jo Grimond.
 It is to date the only occasion since the Second World War when a government has managed to increase its overall majority whilst seeking a third term in government.
 However, despite this success, the Conservatives failed to win the most seats in Scotland, and have not done so since; this marks the beginning of Labour's domination of Scottish seats at Westminster, which lasted until the rise of the Scottish National Party at the 2015 general election.
 Both future Liberal leader Jeremy Thorpe and future Conservative leader and eventual Prime Minister Margaret Thatcher first entered Parliament at this election.
The Profumo affair was a British political scandal that originated with a brief sexual relationship in 1961 between John Profumo, the Secretary of State for War in Harold Macmillan's government, and Christine Keeler, a 19-year-old would-be model.
 In March 1963, Profumo denied any impropriety in a personal statement to the House of Commons, but was forced to admit the truth a few weeks later.
 He resigned from the government and from Parliament.
 The repercussions of the affair severely damaged Macmillan's self-confidence, and he resigned as prime minister on health grounds in October 1963.
 His Conservative Party was marked by the scandal, which may have contributed to its defeat by Labour in the 1964 general election.