In a demonstration of both interest in and confusion about President Reagan's Strategic Defense Initiative, or "Star Wars" antimissile defense, hundreds of British scientists and industrialists turned up here this week for a crowded U.S. briefing on the prospects of SDI contracts.

The briefing, given by Lt. Gen. James Abrahamson, head of the U.S. SDI office, was the first such classified session held in Europe. In a news conference before the meeting, Abrahamson said "Britain's involvement could run into hundreds of millions of dollars over a period of time."

Despite an agreement signed between the two governments last December outlining the terms for British participation, few British companies have signed up. The Defense Ministry originally estimated that Britain could win as much as $1.5 billion worth of contracts.

Although newly appointed British Defense Secretary George Younger said today that more contracts were due shortly, only about $2 million have been won here thus far. The largest of these is a recent agreement signed with Culham Laboratory, part of the government's Atomic Energy Authority, to help design and test a high-voltage particle accelerator.

Abrahamson said his briefing was designed to begin removing some of the impediments to further contracts by providing more of the secret information that companies here say they need to bid on specific contracts.

The meeting was British industry's first look at the still secret bilateral SDI agreement. It outlined 18 areas of British scientific expertise and set up an umbrella structure to deal with such issues as technology transfer and patent ownership for work developed under SDI contract.

Industry officials have complained that they have been denied access to information crucial to preparing the "white papers" the United States requires for preliminary contract queries.

According to an official, the British government also is interested in more information on broader aspects of the $26 billion SDI research program, including an update on its overall progress, its timing and possible budgetary problems.