The couple whose three foster children were removed because of their membership of Ukip want the youngsters back and a public apology.
The pair, who have not been identified to protect the trio of EU-migrant children, lost them when Rotherham Council social workers discovered their political allegiance which they deemed incompatible with caring for the youngsters.
The decision caused a storm of criticism and the Labour-run local authority announced it would investigate the procedures that led to the decision.
The foster couple, who live in South Yorkshire, said in an ideal world they would like the children back but their chances have been wrecked because they do not want to cause them any more upheaval.
The wife told the Daily Telegraph: "We feel that we have personally been slandered and we would like a public apology from Rotherham. We would also like something in the form of a letter stating that they have got it wrong in this case and that it will not be on our records that we have had children removed from our care. We just want a clean slate."
The couple, a qualified nursery nurse and a former Royal Navy reservist, initially spoke out after being told by the social worker that Ukip was a racist party.
Council leader Roger Stone announced on Saturday that the authority would investigate what had happened after mounting condemnation from political leaders including Education Secretary Michael Gove and Labour leader Ed Miliband.
Mr Stone said: "We are going to investigate to make sure everything has been done professionally.... We are looking to make sure all the correct procedures were carried out before the decision was made." It is not known how long the investigation will take.
Education Secretary Michael Gove said social workers had made "the wrong decision in the wrong way for the wrong reasons" and that he would be personally investigating and exploring steps to "deal with" the situation. The politician, who heads the government department responsible for children's services and who was himself adopted as a child said: "Rotherham Council have made the wrong decision in the wrong way for the wrong reasons.
"Rotherham's reasons for denying this family the chance to foster are indefensible. The ideology behind their decision is actively harmful to children. We should not allow considerations of ethnic or cultural background to prevent children being placed with loving and stable families."