Saudi Arabia ordered the British ambassador in Jeddah to return home today because of a "shameful" film depicting the execution of an adulterous Saudi princess and her commoner paramour shown April 9 on independent British televison.

The Saudi government, meeting un-Crown Prince Fahd, also reviewed Britain's economic relations with the wealthy oil kingdom, including the work of British firms in the lucrative Saudi market, according to an account relayed by the official Saudi news agency.

Although the marching orders for Ambassador James Craig fell short of a break in diplomatic relations, the threat of economic sanctions was seen as a measure of the growing indignation in Saudi Arabia and other Islamic states over the two-hour film, entitled "Death of a Princess."

It also was interpreted as a warning to other countries, including the United States. The Public Broadcasting System plans to make the film available to its affiliates May 12. The $430,000 production also received part of its financing from a PBS outlet in Boston, WGBH.

[In Washington, PBS officials reiterated their intention to go ahead with the film, which received funding indirectly from the U.S. Congress. The State Department reportedly has inquired into the number of stations likely to carry the program. Details Page D 1.]

The government-guided Saudi press has been waging a strong campaign against the film, reflecting anger within the Saudi royal family at what editorialists have labeled an affront to Islam inspired by Zionists in the Western media.The reserved Saudi leadership, never at ease with the free-wheeling Western press, has been particularly suspicious since the wide coverage accorded to the Nov. 20 takeover of the Grand Mosque at Mecca by a well-armed band of Islamic dissidents.

Since the Mecca violence, which lasted two weeks and left about 250 dead, Saudi and other hereditary rulers in the Persian Gulf region also have been going out of their way to present an image of Islamic orthodoxy. Their concern has been heightened by fears that Iran's revolution -- using Moslem principles against the monarchy -- could become contagious.

The governments of the United Arab Emirates, Qatar, Bahrain and Oman have expressed solidarity with Saudi outrage at the film. They could be expected to follow the Saudi lead in any economic sanctions against Britain for failing to halt the broadcast on London's nongovernment Associated Television network.

This could cause problems for British construction, consulting, arms and other companies with sales and projects that have brought 30,000 Britons to work in Saudi Arabia alone. Although the film also was shown on Dutch television last week despite Saudi entreaties, there was no mention of the Netherlands in the agency's account of a statement by Saudi Information Minister Mohammed Abdo Yamani.

Saudi Arabia provides about 10 percent of Britain's oil needs. But there was no word of an oil boycott. The Saudi ambassador in the Netherlands, Sheik Ziad Mohammed Ali Shawaf, specially ruled out such a step in seeking last week to keep the film off Dutch television.

The film's producers, Associated Television, described it as a dramatized documentary, much of it filmed in Egypt with Egyptian actress Suzanne Abu Taleb playing the lead. The story recounts the 1977 rebellion of young Princess Misha, the granddaughter of Prince Mohammed, who tried to live with a Saudi lover she had met as a student in Beirut. In the film, he is shown kneeling in a parking lot as an executioner prepares to chop off his head beside the body of Princess Misha, shot by a firing squad for adultery.

Saudi press comment has described this scene as implied criticism of the Koranic law that forms Saudi Arabia's constitution. Under it, an adulteress can be punished by death but only after rigorous and complicated proofs that make such executions rare.

Some reports say Saudi leaders were even more incensed at scenes implying lesbian activity among Saudi women confined to their houses by the strict Moslem marriage rules and at other sequences suggesting that some Saudi women take lovers.

"The British TV film was full of nonsensical lies and all sorts of distortions against Islam and the heritage and traditions of Moslems," said the Saudi newspaper Al Jazirah in an editorial last weekend. It denounced the British government's stand on the film and said, "It will not be allowed to escape without paying the price."

In the face of Saudi indignation, the British foreign secretary, Lord Carrington, cabled the Saudi government last week expressing regret at displeasure the film caused in the kingdom. But the Foreign Office pointed out that the British government had no power to control the content of programs on the commercial network.

Such explanations were difficult to accept in a country where the royal family exercises close control over what appears in the privately owned, government-run Saudia television. In the Arab world, the Anglo-Saxon tradition of a press and television free from government domination is little known.

Craig, a highly reputed Arabist, was called off a vacation in France last week to return urgently to Jeddah to deal with the crisis created by the film. His explanations apparently proved inadequate, however, and Fahd called the royal Cabinet into session last night to review the dispute "in the light of the British government's negative attitude toward the screening of the shameful film," the Saudi news agency quoted the Saudi information minister as saying.

"The Cabinet decided to delay presentation of the credentials of the new Saudi ambassador to Britain. Consequently, there is no need for the British ambassador in the kingdom at present," he added.