British twins who had been separated at birth learned that they were siblings only after they had tied the knot.
The nuptials have been annulled after a High Court judge ruled the marriage had never validly existed.
The couple's identities have been protected for legal reasons.
Their case was first highlighted by Lord Alton of Liverpool during a discussion on donor conception in the House of Lords in December, but only came to light on Jan 11.
The peer told the House of Lords that a court annulled the union as soon as the twins' true relationship became known.
Lord Alton insisted the Bill, to be voted on in the House of Lords on Jan 15, should legislate that birth certificates include information on genetic parents as well as whether the child was conceived by a donor.
The right to anonymity for donors was removed in April 2005, allowing children to identify genetic parents at age 18.
At the same time, there is no legal obligation for parents of donor-conceived children to tell them.
"The state is colluding in a deception. We are opening the door to more cases like this one," The Scotsman quoted Lord Alton, as saying.
"One of the most fundamental things of all is to know who you are. The issue here is about human rights. A birth certificate that omits any mention of your true origin falsifies your history in a very significant way," he added.