The commissioner also insisted she had not obstructed investigators examining how the Met dealt with the 1987 murder of Daniel Morgan.
Led by Baroness Nuala O’Loan, a panel found this week that the Met had made protecting its own reputation a higher priority than finding Morgan’s killer.
Its report said: “Concealing or denying failings, for the sake of the organisation’s public image, is dishonesty on the part of the organisation for reputational benefit and constitutes a form of institutional corruption.”
The force admitted in 2011 that the grossly inadequate first investigation into Morgan’s murder, during which the murder scene was not searched and was left unguarded, had been hampered by corruption.
But Baroness O’Loan’s team found corruption had persisted after that, and questioned why no action had been taken to bring those who sabotaged the first investigation to justice.
Dame Cressida told reporters on Wednesday: “I don’t believe we are institutionally corrupt. No, I don’t accept that. I have the deepest feelings for Daniel Morgan’s family. They have shown extraordinary grit and determination and courage.
“Yesterday, I apologised again to them for our failings and the fact that we have not brought anybody to justice despite six investigations and countless other reviews and pieces of work.
“And for the fact that, in so doing and along the way, we have clearly ... caused them extra anguish.”
Priti Patel, the home secretary, has written to the commissioner to demand answers. She also described the Morgan affair as one of the most “devastating” in the Met’s history.
Dame Cressida was criticised in the 1,200-page report for initially denying the panel access to the police Holmes database while it investigated the case.
She said: “I didn’t obstruct their work. I set out with my team, who were well resourced, to ensure that we gave the panel maximum cooperation, and that we did full disclosure, as quickly as we could.
“I look back and know that I acted with integrity, and that I was at all times trying to fulfil my duty there to the family and to the panel.
“Having said that, I look back and think that in the Met, with this very difficult and powerful report landing, we should of course, together with the Home Office and others, look at what happened during that period, and see whether there are any lessons to be learned for any future possible similar panel.
“Because we would want, of course, to work as effectively as possible with them and have as good communication as possible with them. But I have no intention of resigning.”
A series of police investigations and an inquest have failed to convict anyone of killing Morgan or any associated corruption in protecting those responsible.
The numerous inquiries are largely down to the campaigning efforts of Morgan’s brother Alastair, who has fought for justice for more than 30 years.
He described this week’s findings as a “historic result” but expressed regret that his mother Isobel Hulsmann, who died in 2017, did not live to see its publication – for which he blames the Met.
Dame Cressida should “absolutely” consider her position, he said.
But Dame Cressida said it was her job to focus on leading the Met through a difficult year and a half.
She added: “My people do very difficult work, they have to make very difficult decisions, often with far too little time, sometimes with far too little information.
“I’m very proud of them. I love my job and I will continue to do it. I’m an honourable person. If I thought I should be considering my position I would be, but I don’t.”
Additional reporting by Press Association