Politicians for nearly half a century had gotten elected and retained popular support by bashing communism and stoking fears of the Soviet Union and its threat to the United States. Ronald Reagan was a master at this tactic. His speech to the House of Commons was part of a pattern, also shown in his campaign ads, featuring a bear that was supposed to be the Soviet Union, and a speech in front of the Berlin Wall where he famously said: "Mr. Gorbachev, tear down this wall!"
Reagan believed the Soviet Empire was a threat, and used Americans' collective fear of that threat to justify new nuclear missile construction and huge defense budgets.
This speech is Reagan's "Evil Empire" speech. Given the fact that this is the subtitle, I would say that he saw it as rather strong. In my mind, it's a bit of a challenge to assess Reagan's words in light of what we now know about how the Soviet Union ended up faring by the end of his term. Some would point to Reagan's genius of vision in the speech, as most of what he called for actually ended up happening. There was a certain prophecy in the ideas that the Soviet Union and the Communist empire could not sustain its drive from both internal and external threats for very long, and that the lure of "Western" ideas such as free press, open elections, and economic competition would be too much to bear on the Soviets and their spheres of influence. Another side of the coin simply suggests that Reagan was doing a great job of communicating to both the British and his own people what we wanted them to believe in terms of committing to his vision and foregoing much in way of domestic challenges such as urban renewal, education funding, and health care reform. Reagan's description of the Soviet Union was one of a lumbering giant that was destined to tip over under the weight of the Western calls for freedom and the internal body politic heeding such calls. He cites the Polish Solidarity uprising as one of many such examples that will spell the end of the Soviet Union. Reagan described the Soviet resistance to the West as futile because the call of freedom is too loud. In addition to this, Reagan cited that the state controlled economy of the Soviet Union is running out of steam, helping to justify his own politics of deregulation in America. Both of these components- political and economic reality- will inevitably cause the death of the Soviet Union. Given such a focus, I would say that Reagan felt that this was a strong statement to make at such an early call of his presidency.