The Boeing jet broke out of a dense fog, leveled off only 200 feet from the end of a rain-slick runway and landed automatically while pilot Dick Yenni monitored a computer but did not flying. It was somewhat disconcerting.

The technological feat of a fully automatic landing was demonstrated for reporters at John F. Kennedy International Airport here as the Federal Aviation Administration fired another round in a sometimes bitter and always expensive struggle with the British over who shall have invented the best precision electronic landing system.

The system for which the FAA spent more than $100 million developing indisputedly worked today. The British get their chance with their eqipment on the Kennedy runway next month.

The British are convinced that the United States has not played fair and have said so loudly through diplomatic and business channels. The "flyoff" beginning at Kennedy and scheduled at two other airports is the result of that complaining, but the FAA experts did not even mention the British system today until they were asked about it by reports.

Both sides are attempting to win approval for something aviation badly needs - an improved, reliable system that will give absolutely accurate guidance information to airplanes in the most critical phase of flight - the approach and landing. Between 70 per cent and 80 per cent of all air craft accidents happen during this phase.

Furthermore, the system will provide that guidance in good weather and bad. A "blind" approach, where visibility simply would not be a factor in whether or not to land, is one bonus.

Today, the standard precision landing system requires a straight-in approach on the runway centerline and makes curved approaches impossible in poor visibility, when flying must be done by instruments.

Under the system demonstrated today, curved approaches are possible in all kinds of weather. Such approaches can be used for noise abatement, as was the one flown here, or to pack more airplanes into limited airspace.

Washington's National Airport provides a good example of how the system might be used for noise abatement. Planes landing to the south at National cannot follow the course of the Potomac River in foul weather because the pilots cannot see the river and their instruments will not keep them over the river's center.

As a result, pilots follow a straightline radio beacon that takes them and their jet noise over the Potomac Palisades.

With the new electronics, it would be possible to program a completely automatic approach that would keep airplanes and their noise over the center of the river as it twists and turns, regardless of the weather.

Both the British and American systems fall under the generic name of Microwave Landing Systems, or MLS. They are so named for the portion of the radio frequency spectrum on which their guidance information will be broadcast.

Both systems provide electronic signals that, when coupled with computers on aircraft, can tell a plane precisely where it is in relation to a runway. Depending on how welleqipped the plane is, the guidance information also can control automatic pilots or automatic landing systems.

The differences between the systems are highly technical. Basically, the American system, called the Time Reference Scanning Beam (TRSB) tells the aircraft where it is by measuring time between the aircraft's location and the runway.

The Birtish system, called the Doppler MLS, provides the same information as the TRSB, but measures differences in frequencies instead of time.

A worldwise standard has been sought so everyone will have the same eqipment and international carriers will not have to invest in several onboard decorders. What has amounted to an international competition has been set up by the International Civil Aviation Organization . A final decisions scheduled in April.

An important committee of ICAO has recommended the American system. That decision, which angered the British, apparently was based on two major factors: total cost and the result of computer simulations of the operating charactieristics of the competing systems.

The computer simulations, done by the Massachusettss Institute of Technology's Lincoln Laboratory, showed that the British system under certain conditions provide false guidance signals.

The British contend that, in the long run, their system will be cheaper.

And on the false signal issue, they say it simply is not true. The computer simulation was based on a model of the Brussels airport. The British went to Brussels, set up their system, flew a live demonstration and proved themselves right.

They challenged the U.S. to do the same at Brussels, and further asked that they be given complete access to the computer data of the Lincoln Laboratory.

Langhorne Bond, the Carter administration chief of the FAA, moderated the dispute in September when the promised Congress that the U.S. would participate in flying tests and promised the British complete access to the Lincoln Laboratory data.

Since then, according to Alexander Gordan-Cumming of the British Embassy, FAA and Lincoln Laboratory officials have cooperated fully. "We believe there must be just one system." he said. "If there is a tie, we are prepared to stand aside."

Both British and American officials agree that there is no significant economic advantage for either party. Each has manufacturing rights for the other's system.

"The position of the FAA is that the better system should be approved," Bond said yesterday.