Mr Webb claims he endured "17 years of lies and deceit" when Lydia Chapman became pregnant by her lover but convinced him that he was the father.
The 47-year-old is now pursuing her, and the man he claims is her daughter's true father through the courts in an attempt to claim compensation from them for the money he spent on raising the girl.
His barrister, Nicholas Mostyn, QC, told the Appeal Court in London that the so-called paternity fraud case raised "profound questions" about a spouse's "duty of candour".
"Honesty and good faith lie at the very heart of the contract of marriage," he said.
The court heard that the woman was conceived during "an act of unprotected sex" between Mrs Chapman and her lover at a hotel in 1985.
But Mrs Chapman, a 45-year-old who lives in Southampton, told her husband that he was the father, and when the baby girl was born she was registered as their child.
Judges were told that when she was just three months old, her mother and her lover met again at a summer barbecue and had sex in a picnic area. They are said to have discussed her paternity and "set out to deceive" Mr Webb into believing he was the father.
Mrs Chapman was described as an "inveterate liar" who for several years had a "fixed and certain knowledge" that her husband was not the girl's father.
She is said to have continued to send him birthday and Christmas cards signed "Daddy" from his "daughter" throughout her childhood.
She allowed him to support the girl financially without receiving a penny in maintenance from her true father, it was claimed.
It was not until the girl was 18 that DNA tests proved that Mr Webb was not the girl's father, and her mother filed for divorce.
Mr Webb first launched a claim for damages against his ex-wife and her lover at Bournemouth County Court, accusing them of deceiving him about who the girl's father was. But this claim – denied by the couple – was dismissed by a judge.
This week, he sought permission to appeal this ruling at the Appeal Court, with his barrister claiming his sense of injustice was so great that he would go all the way to the House of Lords, the nation's highest court, if necessary.
However Mr Webb, who lives in Chippenham, Wilts, was thwarted by leading judges, who said his prospects of success were slim under existing law and so it would be "disproportionate" to allow him to proceed with the case.
Lord Justice Thorpe admitted the case raised "interesting socio-legal arguments".
But he added that if it went ahead, it would "visit upon the litigants huge burdens, both financial and emotional, which are disproportionate to any prospects of success".
The judge, sitting with Lord Justice Aikens and Mr Justice Bennett, concluded: "This whole case can be categorised as a misfortune to all those engaged in it. I would not wish to be the one to extend their misfortunes further."
The only option remaining to Mr Webb is to try to take his case to the European Court of Human Rights.
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