According to the Guardian, Judge Justice Hayden drew the legal battle to a close at a private hearing in London on Monday.
He said the woman had decided that pursuing her contact application would be “emotionally harmful” to the children.
He described the family as “courageous” and said he hoped they could move forward.
The judge said the full details of the case could not be reported but added the public should know that litigation had come to a close.
The parent's withdrawal comes after the Court of Appeal overturned a 2017 High Court decision that prevented her from having face to face contact with her children.
The court ruled that “the best interests of these children seen in the medium to longer term is in more contact with their father if that can be achieved.
“So strong are the interests of the children in the eyes of the law that the courts must, with respect to the learned judge, persevere. As the law says in other contexts, ‘never say never’. To repeat, the doors should not be closed at this early stage in their lives.”
The High Court decision followed a Manchester family court's ruling that the transgender parent should not have direct contact with her five children, then aged three to 13, because of fears that the children would be marginalised or excluded from the Charedi community.
Indirect contact, such as writing to the children on their birthday, was permitted.
The Court of Appeal's judgment meant that the case was sent back to the family court, to be heard by a different judge.
