The first time I had to investigate an allegation of sexual assault, it was a young boy who came into a police station in South Yorkshire. I listened to him with an open mind and investigated his account. His attacker was convicted and sentenced to two years in prison.

Thirty years on, the Metropolitan police are investigating many historical allegations. A dam burst after Jimmy Savile died and one of my senior officers stood outside Scotland Yard and said: “Come forward, we will believe you.” And many have: men and women who say they were abused as children or are reporting recent rape or sexual assault allegations, where growing confidence among victims is just as significant. But many women still don’t come forward. The public inquiry, chaired by Lowell Goddard, may bring forward many more allegations.

But how should the police respond, especially when, as in Operation Midland, the allegations are decades old, and suspects are in the public eye?

Investigating these cases is exceptionally difficult. Victims are often damaged by their experience and rarely disclose everything until they begin to trust officers. The passage of time makes it difficult to prove or disprove the allegations. If there’s only one complainant at first, the only way to find corroboration is to investigate and go where the evidence takes you.

Those investigated are innocent until proven guilty, but reputations may be tarnished before we have been able to reach a conclusion. This is distressing for those who are investigated, and for their families, which is why we expressed our sympathy to Lord Bramall.

I recognise that public confidence has been affected by such cases. Yet, confidentiality means we cannot explain our actions in detail. What I want to do instead is look ahead to see if there is a better way to handle historical investigations involving public figures.

First, I believe the time is right for suspects facing allegations of sexual offences to be offered anonymity prior to any charge.

Why? By the time we charge somebody, we must have sufficient evidence to believe the chance of convicting them is broadly greater than 50%, and justice should be open. But the bar is necessarily much lower at the start of an investigation. Even an arrest only requires reasonable suspicion. During an investigation, we have to track down witnesses and are obliged to provide complainants with information, so journalists will, in all probability, find out the names of public figures who are suspects.

To ensure that a suspect is treated fairly, I would only allow police to name them in a sexual assault case after an application to a court, so that a judge can assess the public interest. The media could argue their case if they wished to name someone, as happens in other areas of the law.

My second proposal is for a clear public statement about our approach to victim testimony in these very sensitive cases. The public should be clear that officers do not believe unconditionally what anyone tells them. They are listened to, sometimes at length, before the decision is made to begin an investigation.

We must be clear about the principle of impartiality at the heart of criminal justice. Dame Elish Angiolini, who has reviewed our approach to rape investigations, made a proposal that should be at the core of this debate. She detailed how our policy has moved over the years. In 2002, the Met said officers should “accept allegations made by the victim in the first instance as being truthful”. A report in 2005 called for a “culture of belief, support and respect”. In 2014, Her Majesty’s Inspector of Constabulary said: “The presumption that a victim should always be believed should be institutionalised.” A complaint of sexual abuse must now be recorded immediately as a crime.

Dame Elish questioned whether it is appropriate, or possible, to instruct an officer to believe. Instead, she said: “It is more appropriate for criminal justice practitioners to remain utterly professional at all times and to demonstrate respect, impartiality, empathy and to maintain an open mind … in the first instance, officers should proceed on the basis that the allegation is truthful.”

I agree, and would add that a good investigator would test the accuracy of the allegations and the evidence with an open mind, supporting the complainant through the process. This is a more neutral way to begin than saying we should believe victims, and better describes our impartial mindset. Emotionally, though, it may not be enough to give victims confidence in our approach.

There’s a tension there that’s hard to reconcile, so I’d like it to be part of the independent review of how we investigate historical cases, which I announced on Wednesday. Police officers are trained to be sensitive to victims and complainants. They deserve public support in a role that requires them to listen to the worst that men and women do to one another and to children. I think we all need to recognise that, do what we can to help, then let them get on and investigate.