Assistant U.S. Secretary of Defense Richard Perle, in a speech here last night, sharply criticized British Foreign Secretary Geoffrey Howe for publicly questioning President Reagan's pursuit of a space-based antimissile defense.

Perle's speech escalated a verbal duel between Washington and London over Reagan's Star Wars project, with the British government backing Reagan's plans for research but seeking to make clear it has serious questions about the possible dangers of going beyond the research stage.

Perle, who was said to be here on a private rather than official visit, told a dinner audience at a conference on "Communism and Liberal Democracy" that Howe's major policy speech last Friday "proved again an old axiom of geometry, that length is no substitute for depth."

"In a mere 27 pages," Perle continued, Howe had "succeeded in rewriting the recent history of the Soviet-American relationship, rendering it unrecognizable to anyone who has charted its course." He accused Howe of "mistaking the unfulfilled promise" of the 1972 U.S.-Soviet treaty limiting antimissile defenses "with the reality that followed," and of a "tendentious and obliquely declaratory manner" in questioning Reagan's Strategic Defense Initiative.

British officials said they could not recall any similar instance in which an official of Perle's rank had publicly rebuked a British foreign secretary.

"It's certainly not the kind of thing that happens every day," said one British official. "However, Perle is quite an unusual assistant secretary and perhaps he felt less constrained on a private visit."

Perle is a key adviser to Defense Secretary Caspar W. Weinberger and has been a spokesman for a tough stance toward Moscow in arms control talks. Perle has also been trying to thwart transfer of western trade and technology to Moscow, another issue that has not endeared him to a number of British ministers and industrialists.

U.S. Ambassador Charles H. Price called on Howe today and a Foreign Ministry spokeman said the Strategic Defense Initiative was discussed.

British officials appeared anxious to play down any idea that a quarrel was developing between Washington and London over the Star Wars project. They said Price's visit was part of a regular series of exchanges.

Another source suggested that Price had "cocked an eyebrow" toward Howe, indicating puzzlement over why Howe had chosen this time, as new U.S.-Soviet arms talks are starting in Geneva, to question the Star Wars project publicly.

Howe's speech, which is known to have caused considerable concern in some quarters of the Reagan administration, was the most comprehensive list of questions and concerns about the initiative voiced publicly by any allied official.

Howe asked if the United States might be building a Maginot Line in space that the Soviets could outflank and whether any shift from offensive deterrence to defense could be managed "without generating dangerous uncertainty."

Howe's speech and Perle's response are being seen here by some diplomats as signs that splits over Star Wars are going to be difficult to submerge, despite interest in a unified western front at Geneva.

In his remarks to the conference here, sponsored by a new group called The Committee for the Free World, Perle accused Howe of being silent on what Perle said was the "enlarging pattern of Soviet violations" of existing agreements.

Perle continued, "In what may earn its place as the understatement of 1985 on the unrelenting buildup of Soviet nuclear forces, Sir Geoffrey observes that Russia's 'historical experience has inclined them towards overinsurance.'

"Even in this city of Lloyd's, [a reference to London's insurance market], I find the concept of insurance a less than persuasive description" of the Soviet strategic nuclear buildup, Perle said.