Scotland Yard has refused to apologise to Field Marshal Lord Bramall over a dropped nine-month investigation into historical claims of sex abuse.
The 92-year-old war veteran saw his home raided after allegations were made by one man, known as Nick, before police admitted there was insufficient evidence and announced on Friday night that they had dropped the case.
Assistant Commissioner Patricia Gallan said: "I fully recognise how unpleasant it may be to be investigated by the police over allegations of historic abuse.
"For a person to have their innocence publicly called into question must be appalling, and so I have every sympathy with Lord Bramall and his late wife and regret the distress they endured during this investigation."
In a lengthy statement, the senior officer said police would be put off investigating claims if they had to apologise when inquiries did not end with a suspect being charged.
"The Metropolitan Police accepts absolutely that we should apologise when we get things wrong, and we have not shrunk from doing so.
"However, if we were to apologise whenever we investigated allegations that did not lead to a charge, we believe this would have a harmful impact on the judgments made by officers and on the confidence of the public.
"Investigators may be less likely to pursue allegations they knew would be hard to prove, whereas they should be focused on establishing the existence, or otherwise, of relevant evidence."
A storm erupted over the force's treatment of the D-Day veteran, with London Mayor Boris Johnson among those calling for him to receive an apology.
Ms Gallan said she will meet Lord Bramall at the end of a wider police investigation into historical abuse claims, called Operation Midland, and explain the force's conduct.
In her statement on Wednesday, she said: "The possibility of an apology has been raised, and I thought it was important for the Metropolitan Police to respond publicly. This is an unusual step for us to take, but I think it is in the public interest for me to explain the dilemmas faced by policing in this regard.
"We have many serious allegations referred to us every year that we have a duty to investigate. It is, of course, a principle of British justice that everyone is equal before the law so that duty must apply equally to all, irrespective of their status or social standing. We always endeavour to investigate impartially and to follow the evidence without fear or favour."
She said the claims against the retired army chief were "one part of a detailed set of allegations" and so it was not possible to clear him "as quickly as we would have liked".
In a letter to the Daily Telegraph on Tuesday, Lord Bramall's son, Nicholas Bramall, called for his father's anonymous accuser to be investigated.
He said the key witness, known as "Nick", had been "peddling unsubstantiated and uncorroborated information" that had left his 92-year-old father's distinguished reputation "tainted with the stench of abuse".
In a statement issued through his lawyer, Normandy veteran Lord Bramall said: "I've got nothing to say, this is purely the police justifying themselves and that's up to them. I am glad to say they have offered a senior officer to come and see me and I am willing to speak to them."