Archer is currently in Wayland prison in Norfolk
Scotland Yard is currently investigating Lord Archer's involvement in the fund, set up for Kurdish refugees in 1991.
But the Red Cross says it had direct control over £2.25m of the fund, and that the majority of the reported £57m total was raised by foreign governments.
Former Conservative MP Emma Nicholson called for the Fraud Squad to look into what happened to the millions alleged to be missing, a few days after the peer was jailed
The millionaire novelist helped organise a concert at Wembley Arena for the Simple Truth fund in 1991.
The Red Cross told an investigation by BBC Radio 4's Today programme that after the concert it was asked to give a global figure for the appeal, which it recorded in its accounts as £57m.
'Misleading'
It says the actual figure raised from the concert was just £1m, and that it can account down to the last detail how the money raised in the UK was spent on aid.
British Red Cross chief executive Sir Nicholas Young said he was "puzzled" by the investigation into Lord Archer, as the peer had never had access to any of the funds raised by the appeal.
"It does puzzle me. This is a story of 10 years ago, an appeal, a fund-raising activity and aid activity 10 years ago.
"We have prepared our own report, which we have sent to the Fraud Squad, but they haven't been to see us yet.
"From our papers it is quite clear that Jeffrey Archer had no access to the funds raised by the British Red Cross.
"None of the funds went missing. We can account for all of them."
Baroness Nicholson says the public had been "misled" about the appeal's success.
She told BBC News 24 that the concert made no money and cost more than £500,000 to stage.
"That is not a fund-raising effort," Baroness Nicholson continued.
"It is perhaps something, however, that got Lord Archer his peerage and regained his tattered respectability at that time."
But in her first interview since her husband was jailed, Mary Archer told the Today programme that Baroness Nicholson was "misled and misleading" and her allegations had caused "real harm".
"It is not right that Jeffrey should have been reclassified as the result of an unsubstantiated and baseless allegation by Lady Nicholson and I hope this will speedily be resolved," she said.
Archer to appeal
"They are very serious allegations, they are entirely without foundation, they have resulted in real harm to Jeffrey and now she seems to have smeared the Red Cross into the bargain."
She said the Fraud Squad had not interviewed her about the allegations, even though she has written to them detailing documents she has about the money raised by the appeal.
Archer said on Tuesday he would appeal against his conviction for perjury and perverting the course of justice at his 1987 libel trial.
The former Tory party deputy chairman, 61, was sentenced to four years' imprisonment last month after being found guilty on two counts of perjury and two counts of perverting the course of justice.
He was cleared of one count of perverting the course of justice.
He was initially sent to the high-security Belmarsh Prison in south-east London, where he spent three weeks before being transferred to Wayland Prison near, in Norfolk, a category C jail.