British Prime Minister Margaret Thatcher displayed steadfast solidarity with President Reagan on East-West arms issues following a two-hour meeting here yesterday, declaring that "Our nerve is being tested; we must not falter now."

Thatcher called Soviet leader Yuri V. Andropov's response to Reagan's latest arms control offers "disappointing and discouraging" and said the deployment of new U.S. missiles in Britain and continental Europe will proceed if no agreement is reached in the Euromissiles negotiations in Geneva by the end of the year. At the same time the British leader refused to accept Andropov's public statement Wednesday as the last word, saying that the negotiations should continue in an effort to stave off the planned deployments or to minimize the extent of them if the deployments begin.

Reagan said the "cordial and productive" talks with Thatcher reflected "the superb relations that exist between our two countries."

Thatcher's whirlwind day, including separate meetings with Treasury Secretary Donald T. Regan and Federal Reserve Board Chairman Paul A. Volcker as well as the long and largely private talk with Reagan, produced what she called "an overwhelming preponderance of agreement" on most issues.

Nonetheless, she told a news conference at the end of her meetings that she had been "not assured at all" by the reaction to her plea that the U.S. budgetary deficit must be brought down because it is keeping interest rates unacceptably high and retarding economic recovery throughout the world.

And remarks about the mission and duration of the multinational peacekeeping force in Lebanon, which includes British troops as well as U.S. Marines, suggested that Thatcher is less willing than Reagan to contemplate a long-lasting military involvement there.

"I'm not prepared to make indefinite commitments," Thatcher said. "I believe our role is a restricted one" which should not include remaining in Lebanon until all foreign forces are out, she said. "We may have a very long stay" if that is the objective, she added.

Secretary of State George P. Shultz and other U.S. officials at times have implied that the peacekeeping troops may be needed until Israeli, Syrian and Palestine Liberation Organization troops are removed from a stabilized Lebanon. Thatcher's comment seemed to reject any such idea.

Despite persistent press questioning, Thatcher did not appear to be concerned by a comment of Vice President Bush that British and French nuclear missiles would have to be considered in some future arms control negotiation with the Soviet Union. Thatcher expressed willingness to contemplate negotiations about British missiles "in a world of far, far fewer strategic weapons" but added that this seems a long way off. While Thatcher was meeting Reagan, White House spokesman Larry Speakes read a statement, which he said Reagan had reviewed, calling Andropov's reaction to the latest U.S. proposals in the Euromissiles negotiations "deeply disappointing."

Thatcher's views of the Soviet Union, as expressed in a speech prepared for a dinner at the British Embassy last night, were close to those recently expressed by Reagan.

"We have to deal with the Soviet Union . . . . But we must not fall into the trap of projecting our own morality onto the Soviet leaders. They do not share our aspirations; they are not constrained by our ethics; they have always considered themselves exempt from the rules that bind other states," she said.