Sir Malcolm Rifkind has vowed that a parliamentary investigation into the involvement of British officials in the torture of detainees by the CIA would be conducted "without fear or favour".

Speaking on the BBC Andrew Marr Show this morning Sir Malcolm, who is chairman of theIntelligence and Security Committee of Parliament, said that he would request information linking UK officials to torture redacted from the official report exposing the abuse of detainees during the 'war on terror' released by the US Senate last week.

"We are going to request the Americans – we cannot instruct the United States government – but we are going to request them, not to see the whole redacted stuff because a lot of it's got nothing to do with the United Kingdom, but any references there may be to the United Kingdom and the United Kingdom's possible involvement in these matters. If that was redacted in the public report, yes, we want to see that," he said.

He said the committee would not spare the embarrassment of current or former officials if found to be implicated.

"If people deserve to be embarrassed, it's our job to embarrass them," he said. And added that if British spies were present during torture they were complicit which "would be quite against all the standards of this country".

Downing Street said that some material was removed from the report at the UK's request for national security reasons.

"In the United Kingdom, anything can only be redacted on national security grounds," said Rifkin. "And if the Prime Minister tried to redact one of our reports simply to prevent political embarrassment, we would make a huge public fuss about it. Now we hope the same principle applies in America. That's what we have to test."

There are calls for a full public inquiry to be conducted into the UK's role in the torture of detainees, with critics claiming that the committee is not sufficiently independent, and lacks the legal authority to compel witnesses to testify. Labour's shadow home secretary Yvette Cooper today joined calls for a public inquiry to be held.

Sir Malcolm said that former ministers could be called to testify.

"We will request any former or serving minister who has a contribution to make to our inquiry to give evidence."

If ministers refuse to appear, it will imply they "have something to hide".

Today, former home secretary Alan Johnson today said that the Labour government had investigated claims of UK complicity in torture, but found no evidence to support them.

"When I was home secretary, when David Miliband was foreign secretary, we didn't just sit there and say 'We'll take what the agencies tell us'," he said.

"We made very thorough investigations. We reported to the intelligence and security committee under its previous chair, Kim Howells, on this. We could find no evidence of British agents being involved."