President Reagan Friday celebrated the Moscow summit as marking a turning point in East-West relations, and said that "a worldwide movement toward democracy" was ushering in "the hope of a new era in human history, and, hopefully, an era of peace and freedom for all."

With British Prime Minister Margaret Thatcher looking on approvingly, Reagan told a resplendent audience in the 15th-century Guildhall here that Soviet leader Mikhail Gorbachev "is a serious man, seeking serious reform." Reagan said that "democratic reform" initiated by Gorbachev was progressing in the Soviet Union and deserved the encouragement and prayers of the West.In a speech that echoed an address he made to members of Parliament on his first visit as president to London six years ago, Reagan asserted that "the tides of history were running in the cause of liberty" throughout the world.

He paid tribute to his friend and fellow conservative Thatcher, referring to her as "a voice that never sacrificed its anticommunist credentials" but had first sized up Gorbachev in 1984 as someone the West could "do business" with.

Responding to the president's warm remarks with a speech of mutual admiration, Thatcher said the Moscow summit had "brought us closer to more stable relations" between East and West and would "encourage the course of history for years to come."

"Indeed, I believe there is now more hope between East and West than ever before in the lifetime of most of us here," Thatcher said.

She said that much of the credit for the improved relationships belonged to Reagan's leadership of the alliance and his confident attempt "to enlarge freedom the world over" throughout his presidency. "God bless America," she concluded, and the audience burst into applause.

In his speech, Reagan said the West was engaged in a "crusade for freedom" that is "not so much a test of bombs and rockets as a test of faith and will." The phrase "crusade for freedom" was used frequently to describe the allied cause during World War II. The allied commander in Europe, Dwight D. Eisenhower, called his wartime memoirs "Crusade in Europe."

Reagan's speech in London six years ago outlined a vision of a world in which freedom ultimately would prevail over "Marxist-Leninist tyrannies which stifle the freedom and muzzle the self-expression of the people."

The 1982 speech was crammed with Cold War rhetoric and gloomy warnings of the power of "totalitarian forces in the world who seek subversion and conflict around the globe to further their barbarous assault on the human spirit."

By contrast, Friday's speech to the Royal Institute of International Affairs was a hopeful report on the march of freedom, especially in the Soviet Union.

Praising Gorbachev's program of "perestroika" (estructuring), Reagan looked forward to the day when Soviet citizens would enjoy "such things as official accountability, limitations on length of service in office, an independent judiciary, revisions of the criminal law and lowering taxes on cooperatives."

"To those familiar with the postwar era, all of this is cause for shaking the head in wonder," Reagan said. "Imagine the president of the United States and the general secretary of the Soviet Union walking together in Red Square, talking about a growing personal friendship and meeting, together, average citizens, realizing how much our people have in common."

Despite this glowing appraisal, Reagan sounded several cautionary notes. He said the West must remain militarily strong and be unafraid to engage in "realism and public candor," which he called "the best way to avoid war or conflict." He said that if free nations "question their own faith in freedom" and fail to speak out against human-rights abuses, "they cease telling the truth to themselves."

Thatcher said Reagan had advanced the cause of human rights when he met with religious and political dissidents in Moscow because he had not flinched "from taking the fight for fundamental human rights to the very heart of the Soviet Union." Speaking directly to Reagan, she said, "Your words in Moscow will have shone like a beacon of hope for all those, wherever they are, who are denied their basic liberties."

The president, who appeared visibly fatigued midway through the summit, seemed relaxed and far more rested Friday.