David Alton, an independent, pro-life member of the Lords, said the brother and sister were granted an annulment after a high court judge ruled that the marriage had never validly existed.
The Catholic politician -- who discovered the case after talking to a judge -- used it to highlight perceived deficiencies in the government's proposed Human Embryology and Tissues Bill, which is currently going through parliament.
The bill is designed to make it easier for lesbian and gay couples to have children through assisted reproduction, recognising same-sex partners as legal parents of babies conceived through donated sperm, eggs or embryos.
But it contains no provision to require the identity of the donor to be disclosed, potentially meaning a child could not be told they were conceived by assisted reproduction.
Alton raised the case of the married twins -- who were born after IVF treatment -- during a debate on December 10, details of which only appeared on Friday.
"There are implications for everybody involved, but the needs of the child will always be paramount, and it is right that we should therefore make the process as transparent as possible," Alton told the Lords.
IVF -- which increases the chances of multiple births -- meant such cases could become more common if the law does not require children to be told they were donor conceived and have access to their genetic history, he said.
"The right of children to know the identity of their biological parents is a human right," he added Friday.
"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."
The identities of the twins and details of their relationship and marriage have been kept secret, but it was known they were separated soon after birth and never told they were twins.
They only discovered they were blood relatives after the wedding.
That is certainly...awkward.