It may not yet be ''Bonnie Ronnie'' for President Reagan with the British.
But the American President did win a genuinely warm reception from members of the Houses of Parliament at the Palace of Westminster June 8 for his rather serious speech on the shared values of the democratic nations and their competition with the totalitarian East.
Mr. Reagan came to a Britain that, despite its preoccupation with the Falklands crisis in the South Atlantic, could still muster the pageantry and spectacle that over the centuries helped a people focus on enduring values through times of stress.
At least for Reagan's two-day London visit the British officially pocketed any show of regret over the recent wobble in US support for the British Falklands position at the United Nations.
The Reagans joined the royal family at Windsor Castle for a ''small dinner'' (38 persons) Monday night, June 7, and a state dinner Tuesday, while a member of the royal household served on helicopter duty in the South Atlantic. And Mr. Reagan rode horseback with the Queen in Windsor's lanes, with Mrs. Reagan following in a four-horse carriage driven by Prince Philip.
''Down to the background clip-clop,'' said a British observer, ''it will look splendid on American TV.''
If the British were expecting a Reagan more interested in the video-projected role of the President than in his office's sober responsibilities, they were surprised by what they heard in the Westminster chamber. The palace hall itself was a remarkable room with wigged dignitaries, gilt statuary of Richard I (the Lion-Hearted, no less) and Edward III, and tapestried walls recounting great English hours at Waterloo and Trafalgar.
Reagan gave what his staff called ''a major foreign policy statement.'' It added a fourth arena - intellectual ideological competition with the East - to Reagan's vision of superpower conflict with the Soviet Union, a contest already launched on strategic, political, and economic fronts.
''Impressive,'' said a member of Parliament after the half-hour noon address, which was delivered in a quiet, understated manner. ''Brilliant,'' said another.
''They like him,'' commented a member of the House of Commons. ''That was an endorsement,'' he said of his colleagues' applause. ''His reputation as a whole will be improved.''
Other British listeners hedged their approval. ''I was glad he put an emphasis on arms control,'' said former Prime Minister Edward Heath on leaving Westminster. He added, however: ''In light of events in Hungary and Poland, you have to be extremely careful in encouraging other countries to revolution.''
The West's own economic challenge was bypassed by Reagan, Heath said. ''Thirty million people will be out of work in the Western democracies,'' he said. ''What they want to know about democracy is when it is going to find them a job.''
Margaret Thatcher, the current prime minister, was less stinting in her critique. ''It was, if I may say so, a triumph,'' she told the President afterward at lunch. ''We are grateful to you for putting freedom on the offensive, which is where it belongs.''
Reagan, in his speech, focused on cold war symbols. ''The Berlin Wall, that dreadful gray gash across the city, is in its third decade,'' he said.
He contrasted totalitarian inhumanities with the ''consistent restraint and peaceful intentions of the West'' during the early postwar years when the West's nuclear monopoly might have been used for ''territorial or imperial gain.'' ''Totalitarian rule has caused in mankind an uprising of the intellect and will, '' Reagan said. ''Any system is inherently unstable that has no peaceful means to legitimize its leaders.''
Reagan proposed an East-West ''competition of ideas and values.'' ''For example, I am prepared to offer President Brezhnev an opportunity to speak to the American people on our television, if he will allow me the same opportunity with the Soviet people,'' Reagan said. He proposed a similar exchange of panels of newsmen on television to discuss major events.
''It's a timeless challenge,'' said Sydney Chapman, MP. ''He's pointed out that all the little troubles we make so much of are as naught compared to the struggle between the democracies and totalitarianism. We ought to be much more aggressive to point out the merits of democracy.''