Western culture in general was infectious behind the Iron Curtain. Even the brief glimpses and access that Soviets and East Bloc citizens had of the West were just as appealing as any appeals to freedom of expression and movement. High echelon members of the Communist Party of the Soviet Union reveled in shopping trips to Paris and London (Raisa Gorbachyova was well known for her penchant for fashionable dress even before husband Mikhail ascended as Secretary General), and bootleg tapes of popular Western music acts were ubiquitous. The logic that trying to deny something makes it more appealing was magnified by the general oppression under Soviet rule.
Frankly, the Beatles and other Western pop culture influences were ultimately more responsible for the fall of Soviet Communism from within than anything done by Johnson, Nixon, Reagan, or Thatcher. You can hold back the tanks, but how do you stop a generation of teenagers from humming a catchy tune.
On the Western front, the writings of Aleksandr Solzhenitsyn (particularly The Gulag Archipelago), backed by extensive research and documentation, undermined any validity of the Soviet regime in the eyes of all but the most obtuse supporters. The lawless and arbitrary abuse of power, extensively documented, demonstrated the utterly criminal nature of the Stalinist and Khrushchev eras.
What killed Soviet Communism was its complete fiscal inviability; Russia was dependent, from the very start, on the agricultural yield of the “lesser” republics, and later on the industrial capabilities of the Warsaw Pact “client states”. However, once economic controls were relaxed (perestroika), social liberties followed as a matter of consequence. The same thing is currently occurring in the Peoples Republic of China, and will likely occur in Cuba once the current cult of personality falls apart. Democratic capitalism (with varying degrees of regulation and socialization) has significant deficiencies in many ways, but still comes out as being vastly superior to any attempt at dogmatic communism.