The Football Association chairman Greg Clarke has pledged to fully investigate claims that clubs suppressed the reporting of child sexual abuse by buying the silence of victims and described the alleged cover-up as “morally repugnant”.

Chelsea announced on Tuesday that they have retained an external law firm to carry out an investigation concerning an individual employed by the club in the 1970s, who is now dead. It is believed the investigation is connected to allegations of historical sexual abuse amid claims in a national newspaper that the club sanctioned a secret payment to a former youth team footballer who accused the club’s ex-chief scout Eddie Heath of child sexual abuse.

“I find it morally repugnant that people would suppress reporting of crimes against children to protect their reputation,” Clarke said. “If anyone has behaved improperly, they will be held to account and that information will be released. The FA will not be part of any cover-up. If a club has behaved badly, they will be held to account.”

Clarke also appeared to acknowledge that compensation may be payable to victims after admitting the governing body is facing one of the biggest crises in its history. But he has also been forced to defend its own inquiry after it was revealed the QC chosen to lead it had previously represented the FA.

When asked to measure the size of the crisis, Clarke, who became chairman of the FA in August, said: “It’s certainly the biggest one I can remember. Institutionally, all organisations in the old days used to protect themselves by keeping quiet and closing ranks. That’s completely inappropriate and unacceptable today.

“It’s appropriate that the FA is in the spotlight here,” he added. “We are the governing body. The criminal investigation takes precedence, because it has to stand up in a court of law and it may take some time. But I don’t think that’s an excuse for the FA to do nothing. We’re doing what we believe we can do today, which is examining the role of the FA, how this information was captured, how it was reported, what decisions were made and when. We will bring information to the public domain as quickly as possible. If the FA looks bad, so be it.”

Clarke confirmed that the FA is working with other stakeholders in the national game, from grassroots level to the Premier League, to ensure the investigations are thorough and that appropriate information is shared. He also admitted that the outcome of police investigations could lead to legal action and compensation. Seven forces are looking into historical allegations of assault with Cambridgeshire police the latest to announce an inquiry.

“When the report comes out there may well be legal consequences and all of us in the game have to deal with that,” Clarke said. “Compensation will be a consequence of the facts that emerge. I am worried about it, but only from the point of view that every pound that goes out in compensation is a pound that won’t go into an artificial grass pitch for a deprived community in the UK.”

The length and full scope of the FA’s own inquiry, which was announced on Sunday, remain unclear. It is understood that the final terms of its remit are likely to be agreed at a board meeting today.

The inquiry is to be led by leading QC Kate Gallafent. Gallafent has previously represented the FA in the high court, but Clarke insisted her analysis will be entirely independent. “We hired an external QC to oversee the process [of an inquiry],” he said. “The conclusions will be her conclusions. They won’t be my conclusions. They won’t be approved by me. [Gallafent] has acted for us and she has acted against us on many occasions as well.”

Clarke also responded to suggestions by the Conservative MP Damian Collins that the inquiry should look beyond historical claims and examine the culture of football more broadly. “Fifty-five thousand people in football went through criminal records checks last year,” Clarke said. “Thirty-five thousand people in football were given safeguarding training But has the problem gone away? No. If one child is failed, then the FA has failed.”