It is thought the pair did not know their relationship when they married
A court annulled the British couple's union after they discovered their true relationship, Lord Alton said.
The peer - who heard of the case from a judge who was involved - said the twins felt an "inevitable attraction".
He said the case showed how important it was for children to be able to find out about their biological parents.
Details of the identities of the twins involved have been kept secret, but Lord Alton said the pair did not realise they were related until after their marriage.
'Truth will out'
The crossbench peer, a former Liberal Democrat MP, raised the couple's case during a House of Lords debate on the Human Fertility and Embryology Bill in December.
"They were never told that they were twins," he told the Lords.
"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."
He told the BBC News website that their story raises the wider issue of the importance of strengthening the rights of children to know the identities of their biological parents.
Adults Affected by Adoption
"If you start trying to conceal someone's identity, sooner or later the truth will out," he said.
"And if you don't know you are biologically related to someone, you may become attracted to them and tragedies like this may occur."
Pam Hodgkins, chief executive officer of the charity Adults Affected by Adoption (NORCAP) said there had been previous cases of separated siblings being attracted to each other.
"We have a resistance, a very strong incest taboo where we are aware that someone is a biological relative," she said.
"But when we are unaware of that relationship, we are naturally drawn to people who are quite similar to ourselves.