At #3, the now-classic 'The Young Ones' by Cliff Richard and the Shadows':
Some memorable events (via Wikipedia):
7 January: A bomb exploded at the Paris apartment building where controversial existentialist author Jean-Paul Sartre lived. Sartre was not home at the time, and his mother was not injured, but the fire destroyed most of his unpublished manuscripts.
An assassination attempt against Indonesia's President Sukarno failed, but the hand grenades thrown at his automobile killed three bystanders and injured 28 others in Ujung Pandang (at that time, Makassar).
8 January: The first two teams of the United States Navy SEALs, were commissioned as the United States Navy's Sea, Air and Land teams, with an order backdated to January 1, in order to carry out President Kennedy's recommendation for the development of "unconventional warfare capability". SEAL Team One, based in Coronado, California served the Pacific Fleet and SEAL Team Two served the Atlantic Fleet out of Little Creek, Virginia. Each team consisted of 50 men and ten officers.
Also, in a closed session at the Presidium, Soviet leader Nikita Khrushchev delivered what was later referred to as the "meniscus speech", using the analogy of a wineglass filled to the point that it could overflow at any time. In the speech, which was not revealed until 40 years later, Khrushchev told the ministers that the U.S.S.R. was weaker militarily than the United States, and that the only way to compete against American superiority was to maintain the threat that world tensions could spill over. "Because if we don't have a meniscus," Khrushchev said, "we let the enemy live peacefully."
9 January: Rashidi Kawawa was appointed as the last Prime Minister of Tanganyika, by President Julius Nyerere, who had formerly had both posts. The position of Prime Minister would be abolished on December 9, after which Tanganyika and Zanzibar had merged to form Tanzania. Kawawa would become the first Prime Minister of Tanzania when that post was created in 1972.
Also, Cuba and the Soviet Union signed a trade pact.
10 January: An avalanche on Mount Huascarán, the tallest peak in Peru killed 4,000 people. At 6:13 pm, melting ice triggered the slide of three million tons of ice, mud and rock down the side of Huascaran, quadrupled in size as it gathered mass, and, within eight minutes, buried the town of Ranrahirca (population 2,700) the village of Yanamachico, and three other villages totaling 800 residents. Ranrahirca, which had only 50 survivors, would be rebuilt, then destroyed again in an earthquake and an even larger avalanche on May 31, 1970.
11 January: Soviet submarine B-37, nine days away from being dispatched to Cuba, was moored at Polyarny, conducting maintenance and pressurizing of outdated gas-steam torpedoes. At 8:20 am, a fire in the torpedo compartment detonated all twelve torpedoes and instantly destroying the submarine. Captain Anatoly Begeba, who had been outside, inspecting the top of the sub, survived. The 78 men inside the sub drowned as it sank to the bottom of the Barents Sea.
Also, piloting the newest model of long-range bombers, the B-52H Stratofortress, crewmembers broke 11 non-stop distance and course-speed records, for its aircraft class and time, when they successfully completed a more-than-21-hour non-refueled flight—flying approximately 12,500 miles across the globe..
Also, Nelson Mandela secretly left South Africa for the first time, as he was driven across the border to Botswana. From there, he went to Ethiopia to speak at a conference in Addis Ababa. He would tour the continent for the next six months. Upon his return to South Africa on August 5, he would be arrested.
12 January: Operation Chopper, the first American combat mission in Vietnam, began as the American pilots transported hundreds of South Vietnamese troops to fight against a Viet Cong force near Saigon. Three days later, President Kennedy told reporters at a press conference that American troops were not being used in combat.
Also, A spokesman for the Army of Indonesia, Colonel Soenarjo, that soldiers had begun landing on West Irian, the semi-independent western side of New Guinea that remained under the administration of the Netherlands.
13 January: With the United States having halted its U-2 flights over the Soviet Union, the Republic of China (Taiwan) began regular U-2 surveillance flights over the People's Republic of China, with a group of American-trained pilots nicknamed the Black Cat Squadron.
Also, Albania allied itself with the People's Republic of China, as the two nations signed a trade pact.
UK chart hits, week ending 13 January 1962 (tracks in italics have been featured previously)