The correct answer is A) Many British colonies sought independence.
The factor that played the most significant role in effecting a major change in Britain following World War II was that many British colonies sought independence.
Let's see some examples.
Jordan gained its independence on May 20, 1946. Pakistan on August 14, 1947. India on August 15, 1947. Myanmar on January 4, 1948. Sri Lanka on February 4, 1948. Sudan on January 1, 1956. Nigeria, October 1, 1960. Sierra Leona on April 17, 1961. Kuwait on June 19, 1961.