The unnamed pair were adopted by different families and neither was told they had a twin. However, when they later met as adults they fell in love and then got married. The marriage was annulled in a private hearing by a High Court judge after the truth became known.
The exact details of the case have been kept a secret, but the case was heard recently in the High Court's Family Division, the Evening Standard newspaper reported on Friday.
Professor Lord Alton, who discovered the case, told the paper that the situation underlined the need for children to have the right to know the identities of their natural parents.
"The right for children to know the identity of their biological parents is a human right. There will be more cases like this if children are not given access to the truth. The needs of the child must always be paramount," he said.
"They met later in life and felt an inevitable attraction, and the judge had to deal with the consequences of the marriage that they entered into and all the issues of their separation."
The one-time Liberal Democrat MP initially spoke about the couple during a House of Lords debate on a Human Fertility and Embryology Bill in December.
