A British couple have abandoned a fight to regain care of their child despite being cleared of abuse at a criminal trial.

The man and woman had complained of being victims of a miscarriage of justice because their child had been adopted when they had not been convicted of any offence.

However, they now say that taking the child away from the adoptive parents would be wrong.

Local authority social services had raised concerns shortly after the child was born, leading to a family court judge making several findings, on balance of probabilities, against the child’s biological parents. The child was placed with prospective adoptive parents in 2014, and was adopted by them the following year.

The couple had also been accused of harming the child and prosecuted. But last year they were acquitted when a crown court judge concluded there was no case to answer.

A senior judge is currently re-examining the case at a hearing in the family division of the high court. Sir James Munby, the most senior family court judge in England and Wales, began analysing evidence in mid-October after the couple challenged the findings made by a family court judge in 2013.

He said the couple had made it clear that if they succeeded in overturning the 2013 findings they would seek a revocation of the adoption order and try to regain care of their child.

On Wednesday, however, Munby revealed that the couple had decided to give up their fight. The judge said both had notified the court that they no longer wished to challenge the family court judge’s 2013 findings. He said the couple had outlined their feelings in witness statements.

“We knew from the beginning that even if the family court cleared us this time, we might not get (X) back,” the mother had said.

“We now know that it is too late to move (X) from the adoptive parents. This would not be the right thing for (X).”

She had added: “I want (X) to know that we would never hurt (X), but I cannot go through [another] long court hearing where I am accused again of lying to cover up hurting (X) or to cover up for (the father) hurting (X).

The father had told Munby: “The idea of taking (X) away from all (X) knows is not something I can live with.

“My overriding concern is (X’s) welfare.”

He had added: “The best way I think I can express my love for (X) now is to make it clear (X) should remain in the care of the adoptive parents.”

Munby said he had decided that the new hearing would continue in spite of the couple’s change of heart. The judge said it was in the child’s interests – and the public interest – that “the truth” was ascertained.

He added that the fairness and validity of the process would not be compromised by the absence of the couple and their lawyers.

Munby said nothing could be reported that might identify the child, including the child’s sex.