Doctors said surgery could allow one twin, known as Jodie, to have a normal life, but that her sister, Mary, would not survive the surgery. If the girls were not separated, doctors said, they would both die within months.
There was no immediate indication when the surgery might be done.
The parents, identified only as Roman Catholics from the Maltese island of Gozo in the Mediterranean, came to Manchester for the Aug. 8 birth of the twins, who were joined at the lower abdomen. The parents had fought the operation, they said, on religious grounds.
At one point, the said they would accept the deaths of both their babies as God's will.
Official Solicitor Laurence Oates, who represented Mary before the Court of Appeal, said he had decided against an appeal to the House of Lords after being notified that the parents did not want to do so.
``As the judgments repeatedly emphasize, (the Court of Appeal's) decision is specific to the unique and tragic facts of this case,'' Oates said.
``I am satisfied that the decision will not set a precedent which would undermine the principles of law deriving from and supporting the respect for the sanctity of life and the belief that all life has equal value, which I have been most concerned to uphold,'' Oates said in a statement.
The Official Solicitor represents minors in court cases.
Three judges of the Court of Appeal ruled Sept. 22 that the case came down to an issue of self-defense-the right of the stronger twin to be released from a sister who would eventually kill them both.
``The sad fact is that Mary lives on borrowed time, all of it borrowed from her sister,'' said Lord Justice Alan Ward. ``She is incapable of independent existence. She is designated for death.''