Rights to publicity about little Louise Brown have pitted the tabloid Daily Mail against Britain's Labor government.

Yesterday the government gave in, thereby preserving the Mail's picture monopoly of medicine's newest triumph - the world's first baby conceived in a laboratory dish.

At issue was a film of the birth made Tuesday night by the government's Central Office of Information. With the permission of Lesley Brown, the baby's mother, two cameras whirled away from start to finish, recording the event for posterity and science.

Before the cameramen were allowed into the Oldham Hospital, however, their director had to sign an agreement with the Mail's syndicate and the Browns, promising to hold the film for 28 days. After the time has elapsed the Mail and its customers will no longer have exclusive rights to the story.

When higher government officials heard of the deal, they were outraged. They asked how a patient enjoying the services of the state-supported National Health Service could agree to let a film be made and then control the government's use of it.

Enthusiastic aides at the Central Office of Information realized they had, in the words of one, "a very hot property." They offered to sell footage to television companies.

An indignant lawyer for the Browns, Paul Vincent, quietly responded with a reminder of the contract's 28-day ban. The government decided this was one fight from which it would be best to back away.

So Health Minister Roland Moyle ordered his department to make a face-saving retreat. It issued a statement saying that "ministers have decided they cannot accept the agreement involving" the Mail syndicate. They will sell film to any buyer, "subject to the views of the parents."

The last provision did it. The Browns and their doctors have received an estimated $550,000 from the Mail, and they will not jeopardize their interest by releasing the film.

Yesterday, the Mail's front page was a portrait of the baby at 18 hours, almost the very moment that gynecologist Patrick Steptoe was berating journalists not connected with the Mail for putting his patient under stress.

Mail readers are likely to be treated to more of the same until the 28 days expire. That the paper means business was evidence by a warning it put out yesterday, threatening to sue anyone who reproduced its contents without permission.

This is not the first time the Mail has beaten a Labor government. In 1924, the paper helped crush Prime Minister Ramsay MacDonald by publishing the doctored "Zinoviev letter," unleashing a Red scare on the eve of an election.

Meanwhile, hospital officials reported yesterday that the baby "was progressing very well" after being moved from a special care unit to join her mother in the maternity ware.

Dr. Steptoe cautioned other infertile women not to pin their hopes immediately on this method of conception.

"It is obvious," he said, "this is not immediately available to everybody."

Dr. Robert Edwards, a physiologist and Dr. Steptoe's colleague in pioneering the method added, "We have a lot to learn."