Answers. Best Answer: In 1965, Ian Smith, the prime minister of the British colony of Rhodesia (now Zimbabwe) issued his famous Unilaterial Declaration of Independence.Britain responded with economic sanctions, the withdrawal of Her Majesty's ambassador to Rhodesia, and effective travel bans on Rhodesian leaders.nswers. Best Answer: In 1965, Ian Smith, the prime minister of the British colony of Rhodesia (now Zimbabwe) issued his famous Unilaterial Declaration of Independence.