Tech firms should make a digital key for police to unlock encrypted messages in “exceptional circumstances” such as child abuse or terror cases, a senior police officer has suggested to an inquiry.

Norfolk Police Chief Constable Simon Bailey, the UK lead for child protection, said the tool would help UK authorities who are already stretched to capacity hunting online predators, the Independent Inquiry Into Child Sexual Abuse (IICSA) heard.

But Melissa Polinsky, a senior executive at Apple, has told the inquiry any such key could be exploited by hackers to harvest the passwords, bank and medical details of hundreds of millions of people.

Mr Bailey, who recently suggested a boycott of social media companies, told the inquiry: “If I know and you know that somebody is abusing a child or sharing abusive imagery, then you surely give up your right to privacy.

“I’d like to be in a position to have that conversation, because end-to-end encryption is going to make an already incredibly difficult task for myself, the National Crime Agency (NCA), so much harder.”

Counsel to the inquiry Jacqueline Carey said: “(Ms Polinsky) is saying that can’t be done yet, so how is it that law enforcement is going to try and get round in a different way the problem that end-to-end encryption poses?”

Mr Bailey replied: “I think there needs to be with these companies some form of key that would afford access, and a very clear understanding from all customers that sign up to the contract that that key to break the privacy would only ever be used in exceptional circumstances.”

A prospective version of the Google Chrome browser will contain end-to-end encryption making it “harder to block harmful content” and “easier, not harder, for child abuse to take place online”, lawyer William Chapman previously told the inquiry.

The inquiry heard of an “exponential growth” in referrals flagging suspected child abuse in the UK, and Mr Bailey said Britain is the third-biggest consumer of live-streamed child sex abuse in the world.

Figures show referrals have jumped in recent years – from 43,072 in 2016 to 82,109 in 2017 and 113,948 in 2018.

Mr Bailey said around 400 suspects are arrested, with around 500 children safeguarded per month in the UK – but forces were at “saturation point”.

Robert Jones, director of threat leadership at the NCA, earlier told the inquiry there was an increase in the “scale, complexity and severity” of child abuse offending.

He said: “We are seeing more and more people pursuing more severe images of young children.

“We don’t see any sign of that demand plateauing, so it seems to be getting worse and you can’t explain all of this by technology and greater access.”

Mr Bailey added: “Levels of depravity that haven’t been seen before are now being seen.”

The referral data comes from the US National Centre for Missing and Exploited Children (NCMEC), which passes it on to law enforcement in countries around the world.

The figures include “non-actionable” referrals, referrals with no identifiable criminal offence, and also contain duplicates.

Globally, the number of referrals recorded by the NCMEC jumped from 110,000 in 2004 to 18.4 million in 2018, the inquiry heard.

The IICSA is conducting its second investigation phase, into how the internet is used to facilitate child sexual abuse in England and Wales through acts such as grooming, sharing indecent images and live-streaming abuse.

Leading tech firms including Facebook, Apple, Google and Microsoft have given evidence on how they are fighting child sexual exploitation on their platforms.