He favoured links with the People's Republic of China, visiting Mao Zedong in Beijing in 1974 and 1975 and remaining an honoured guest in China on frequent visits thereafter and forming a close relationship with Mao's successor Deng Xiaoping. Heath realised that to become closer to Europe he needed to be further from the United States, so he downplayed the Special Relationship that had long knitted the two nations together. The two nations differed on such major crises as Britain's EC membership, the Nixon economic "shocks" of 1971, the war between India and Pakistan, détente with Russia, Kissinger's Year of Europe and the Middle East crisis of 1973.
Heath was targeted by the IRA for introducing internment in Northern Ireland. In December 1974, the Balcombe Street ASU threw a bomb onto the first-floor balcony of his home in Wilton Street, Belgravia where it exploded. Heath had been conducting a Christmas carol concert at Broadstairs and arrived home 10 minutes after the bomb exploded. No one was injured in the attack, but a landscape painted by Winston Churchill – given to Heath as a present – was damaged.
Heath tried to bolster his government by calling a general election for 28 February 1974, using the election slogan "Who governs Britain?". The result of the election was inconclusive with no party gaining an overall majority in the House of Commons; the Conservatives had the most votes but Labour had slightly more seats. Heath began negotiations with Jeremy Thorpe, leader of the Liberal Party but, when these failed, he resigned as Prime Minister on 4 March 1974, and was replaced by Wilson's minority Labour government, eventually confirmed, though with a tiny majority, in a second election in October.
In the 1960s, Heath had lived in the Albany, off Piccadilly; at the unexpected end of his premiership, the French couple living there refused his demand that they move out so that he could have his flat back ("So much for European Unity!" Heath later wrote in his memoirs). For four months, Heath took the flat of Conservative MP Timothy Kitson; Kitson declined his offer to pay rent but later recalled an occasion when his own watch broke, and Heath in response invited him to take one of a large collection that he had been given on his travels. In July 1974, the Duke of Westminster, a major London landowner and ardent Europhile, allowed Heath to rent a property in Wilton Street, Belgravia, for an annual rent of £1,250 (just under £10,000 at 2014 prices), a tenth of the market value. The house had three storeys and a basement flat for Heath's housekeeper, and he continued to use it as his London home until old age prevented him from climbing the stairs.
Heath was a supporter of the Lancashire football club Burnley, and just after the end of his term as prime minister in 1974 he opened the £450,000 Bob Lord Stand at the club's Turf Moor stadium.
Lord Armstrong of Ilminster, who was Heath's friend and former Private Secretary, stated his belief that Heath was asexual, saying that he "never detected a whiff of sexuality in relation to men, women or children." Another friend and confidant, Sara Morrison, former Vice-Chairman of the Conservative Party, said Heath had "effectively" told her "that he was sexless". Charles Moore, in his authorised biography of Margaret Thatcher, said that Bill Deedes believed that Thatcher "seem[ed] convinced" Heath was gay, whilst Moore believed it is "possible" that Thatcher's reference, in interview in 1974, to Heath not having a family, was a deliberate hint that he was gay, in order to discredit him.