The fate of a 6-day-old baby girl, whose birth to Britain's first known paid surrogate mother has stirred a demand to outlaw such practices, is now in the hands of a judge who must decide whether to let the child be united with a childless couple who paid for the surrogate.

The child was reportedly conceived by artificial insemination by the would-be father. The couple, whose identities have not been revealed, are said to have paid about $16,000 for the arrangements through the British branch of an American commercial agency. The couple have been reported to be Americans, and the judge's decision may therefore also involve the question of whether the baby can leave the country.

At the moment, there are no legal bans here against such practices. Because of this, and the unprecedented nature of the situation, several officials and public figures who sharply condemn such practices have suggested that in this case, the best interests of the child would be served by allowing her to be united with her prospective parents, assuming, as Health Minister Kenneth Clarke put it, that she would be in "a loving home." But the child, at least for now, is a ward of the court until the judge of the Family Division of London's high court decides what should be done.

The legal confusion and human drama surrounding the case began to unfold soon after the 7-pound 13-ounce girl was born last Friday to the surrogate mother, 28-year-old Kim Cotton of Finchley, who has two children of her own.

When the maternity hospital at Barnet, outside London, was given no details about the child's father, the local community's social services council secured a court order that the child be kept in what is called "a place of safety," meaning the hospital. The council said it was concerned that the child might not be properly cared for or might be moved out of the country.

Several public figures, including Clarke and Lady Warnock, who had headed an inquiry that recommended outlawing commercial surrogacy, have criticized the local council for interfering because no illegal act had been committed. The critics said the episode could scar the parents and, ultimately, the child if their identities are disclosed.

Before the council could make any further decisions, possibly including putting the child up for adoption, the high court took over the case. While it has not been disclosed who asked the court to intervene, there were unconfirmed reports today that the request was made by the father.

The argument against what are being called "rent-a-womb" schemes here is that it "imposes a means test on parental suitability," as the Manchester Guardian put it, exposing low-income women to exploitation by wealthier couples.

As her share of the fee, Cotton was reportedly paid about $7,500 by the Surrogate Parenting Center of Great Britain in Surrey, which negotiated the deal with her. The year-old center is a branch of the National Center for Surrogate Parenting in Chevy Chase, Md.

A spokeswoman for the U.S. firm said it had arranged 16 surrogate births in the United States, out of an estimated 200 reported since 1980. The firm's founder, Harriett Blankfeld, is now in England and was not reachable. In a 1983 interview with The Washington Post, Blankfeld said, "My goal is to have offices around the country and maybe in England, the Middle East and Western Europe. I want to see this company become the Coca-Cola of the surrogate parenting industry."

William Handel, a Los Angeles attorney who directs an information clearing house on surrogate births and has arranged 29 such births in the United States, said there is no law regulating the issue anywhere in the world. Handel said that because of the English legal climate on the question, "I would never let a child be born in England."

Cotton, the surrogate mother, has signed an exclusive agreement, reportedly for more than $20,000, with London's tabloid Daily Star newspaper for her story. Cotton said she wants the money to improve her home and this, too, has added to public criticism.

Clarke said that government ministers will be meeting soon to discuss legislation that would make commercial surrogacy illegal. But he said that where there is only a purely voluntary arrangement, in which no money changes hands, "I personally fail to see how the law can step in and stop that."