Dame Elizabeth Butler-Sloss, the country’s most senior woman judge, told the white couple that they would have to adopt to establish their legal rights. She ruled that, in the eyes of the law, the legal father is the black man whose sperm was mistakenly mixed with the eggs of the white mother.

The twins at the centre of what the judge described as a tragic human story will still be brought up by their “loving” white parents. Dame Elizabeth said: “Everyone concerned with the problems which have arisen agrees that the twins should remain with the family into which they were born.”

The white couple, known only as Mr and Mrs A, who have cared for the twins since their birth and have a residence order in their favour, could seek to adopt so as to make Mr A the legal father, the judge said. “In my judgment the twins’ rights to respect for their family life with their mother and Mr A can be met by appropriate family or adoption orders and those orders would be proportionate to the infringements of those rights,” she said.

“Although they lose the immediate certainty of the irrebuttable presumption that Mr A is their legal father, they will remain within a loving, stable and secure home. They also retain the great advantage of preserving the reality of their paternal identity.”

Although the ruling gave backing to Mr B as the legal father of the babies yesterday, in practice his rights are limited and are akin, as the judge put it, to those of an “unmarried father”. He does not therefore have automatic parental responsibility, which would give him rights over decisions affecting the children’s future, unless the natural mother, Mrs A, agrees to this or a court orders it.

But Dame Elizabeth, who is President of the High Court Family Division, said that Mr B had indicated that he would not be applying for such an order. Instead, he may apply for contact with the babies, as part of any adoption made in favour of Mr and Mrs A.

So far his contact with the twins had been “non-existent”. He was the biological father in circumstances in which he had had no opportunity to forge any relationship with them, the judge said.

The babies were born after a procedural blunder at the assisted conception unit of Leeds General Infirmary when the sperm of Mr B was mistakenly used to fertilise the eggs of Mrs A. None of the individuals in the case can be identified but Leeds Teaching Hospitals NHS Trust Health Trust was publicly named by Dame Elizabeth at a hearing last year.

The hospital trust could now face an unprecedented claim from both couples for damages, although any sums awarded could be small.

Andrea Dyer, solicitor for Mr and Mrs A, confirmed that the couple would be seeking to adopt. “The couple feel blessed that they have two beautiful children and Mr A will continue to treat them as his own,” she said. “They feel a great deal of sympathy for Mr and Mrs B.”

Mohammed Ayub, solicitor for Mr and Mrs B, praised Mr and Mrs A for their “sensitivity and understanding”. He said that his clients wanted time to reflect before deciding what to do.

Dame Elizabeth said that behind the case was the “tragic human story” of two couples trying to come to terms with a mistake. “Through no fault of theirs, they have been born children of mixed race by a mistake which cannot be rectified,” she said. “Their biological mother and their biological father are not married and cannot marry. They may not be able during their childhood to form any relationship with their biological father.” The twins needed love, security and protection within their existing family, she said.

She had been asked to rule on whether the biological father, or the husband of the white mother and the babies’ social father, was the legal father under the Human Fertilisation and Embryology Act 1990.

Laurence Oates, the Official Solicitor acting for the children, said that the judgment was “a step in the direction of resolving . . . the real human dilemmas behind the mistake that has occurred in this case”.

It had established the legal parameters and effectively made clear that Mr A was not entitled to be treated as the legal father by virtue of the Act.

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