The tests were being sought by a man attempting to prove the girl, born after his affair with a married woman, is his child.
The woman, named only as Mrs F, said her husband was the father, although she accepted that, at the time of conception, she was also having a sexual relationship with the other man. She and her husband are bringing up the girl, the court was told.
In an appeal against an earlier High Court ruling, the applicant, known as Mr B, argued it was best for the child to know the identity of her natural father. 'It must inevitably be in . . . (the child's) interests to know the truth about her parentage,' he said.
He argued that in the future, the girl could unwittingly marry a blood relation. Further, he said that she could develop a disease for which treatment depended upon knowledge of her genetic make-up.
The man had started court action in an attempt to establish parental responsibility and, with it, his right to see the child. But Lord Justice Balcombe, sitting with Lord Justice Nolan and Lord Justice Kennedy, dismissed these arguments, pointing out that the girl had been brought up 'as a child of the family of Mr and Mrs F'
Lord Justice Balcombe said: 'Now, and for the first few years of her life, . . . (the child's) physical and emotional welfare are inextricably bound up with the welfare of the family unit of which she forms a part: any harm to the welfare of that unit, as might be caused by an order for the taking of blood tests, would inevitably be damaging to (the child).'
He cited part of the High Court judgment, where Judge Clive Callman had said it was 'unfair to expose this infant to the risk of losing the presumption of legitimacy that she has up to now enjoyed'.
Judge Callman had given 'more weight to this factor than is appropriate in modern circumstances, but this does not detract from the main thrust of his judgment', the Court of Appeal said. Anything that disturbed the stability of her family would be 'detrimental' to the child.
Afterwards, the applicant accepted that under the Children Act the child's interests in any court proceedings were of overriding importance, but said: 'My argument . . . is to do with the truth. What the court is saying is that it is all right for this child to go on being told things about her origins which those telling her know are almost certainly untrue.'
He had started the action because 'I feel I'm being deprived of my daughter and - if it doesn't sound too egotistical - my daughter is being deprived of me'.
The Children Act had appeared to ensure that a child would be brought up by 'two natural parents', but in practice 'it still seems to be so much in favour of the mother', he said. In future, mothers would be able to say 'I don't want this man to be declared the father.'
He is considering an appeal to the House of Lords, but with the court ordering him to pay both sides' costs, he faced a bill for many thousands of pounds, which he says he cannot afford.