Britons must accept a greater loss of digital freedoms in return for greater safety from serious criminals and terrorists in the internet age, according to the country’s top law enforcement officer.

Keith Bristow, director general of the National Crime Agency, said in an interview with the Guardian that it would be necessary to win public consent for new powers to monitor data about emails and phone calls.

Warning that the biggest threats to public safety are migrating to the internet and that crime fighters are scrambling to keep up, the NCA boss said he accepted he had not done a good enough job explaining to the public why the greater powers were necessary.

“What we have needs to be modernised … we are losing capability and coverage of serious criminals.”

But the boss of the organisation known informally as Britain’s FBI warned that support must be gained from the public for any new powers that would give the state greater access to communications data, dubbed the “snoopers’ charter” by critics.

He said: “If we seek to operate outside of what the public consent to, that, for me, by definition, is not policing by consent … the consent is expressed through legislation.”

He added that it was necessary to win “the public consent to losing some freedoms in return for greater safety and security”.

Last week the home secretary, Theresa May, backed the introduction of greater mass surveillance powers, and committed the Conservatives to implementing the communications data bill that had been blocked by the Liberal Democrats amid protests over civil liberties.

Bristow warned it would be wrong to grant the greater powers to access email and call data without public agreement. Some may see that as an implicit criticism of how previous secret mass surveillance powers, revealed by the US whistleblower Edward Snowden, were enacted.

The NCA boss said Snowden’s leaks, principally to the Guardian, were a betrayal. He said he thought the concerns about excessive government invasion of privacy and secret mass surveillance programmes were legitimate. But he thought once the need for greater surveillance was explained, the public would understand. Bristow said loss of privacy concerned him too: “I recognise there is a tension and a balance.”

Bristow accepted that it would be harder now to win support for greater surveillance powers. “The Snowden revelations have damaged public confidence in our ability, whether it’s law enforcement or the intelligence agencies, to access and use data in an appropriate and proportionate way.”

The National Crime Agency was set up by the coalition to spearhead the national response to serious and organised crime. It has been called Britain’s version of America’s FBI with ministers considering giving it even greater powers and handing it the lead role in counter terrorism. It replaced the Serious and Organised Crime Agency, which was beset by problems from its birth.

Bristow’s seniority as head of the NCA is such that he has the power in law to direct the work of other police chiefs, including Sir Bernard Hogan-Howe, the Metropolitan police commissioner.

Bristow insisted his agency had got off to a strong start. In the interview he told the Guardian that:

• A series of scandals such as allegations of corruption in the handling of the Stephen Lawrence case had left policing’s reputation damaged and lower than it had been in years. “I think our stock … the esteem in which we are held … is in my judgment not where it was a few months or years ago,” he added.

• He could see “advantages” if the government stripped Scotland Yard of its leadership of the fight against terrorism, as the capabilities and tactics in fighting organised criminals and terrorists are often the same.

• The US pullout from Afghanistan was predicted by his experts to lead to an increase in the amount of heroin heading to Britain’s streets.

Speaking before the home secretary’s conference speech, Bristow argued that cybercrime posed a threat to Britain’s national security and way of life, and that powers he had to investigate criminals using modern technology were inadequate and needed boosting.

Bristow said law enforcement organisations investigating suspected paedophiles and drug and human traffickers were now operating in a digital world, and needed the ability to prove a communication took place between identified persons at a particular time and place. “We are running some very serious risks. This is about public safety – we need the powers to do our job in a digital age. We need to set out our case,” he added.

Bristow said cybercrime posed a direct threat to national security, and even to Britain’s way of life. The NCA was leading new ways to tackle cybercrime: ”Some of the cybercriminals we are dealing with, it’s not as easy as finding a door that we can kick in.”

The NCA launched in October last year, led by Bristow. He was for some a surprise choice of the job, having previously been the chief constable of the small Warwickshire force.The government is considering stripping the Met of its national lead in counter-terrorism and handing it to the NCA. In the interview Bristow for the first time commented on the advantages of such a radical shake up, which Scotland Yard is resisting. He said terrorists and organised criminals often operate in the same way and that “the tactics of law enforcement to tackle these people are often the same”.

Bristow, formerly chief constable of the small Warwickshire force, said that in a time of austerity it would be sensible to look at shared capabilities with Scotland Yard to tackle the twin threats. “The judgment that will need to be made is how do we get best effect out of our collective effort against terrorists and organised criminals … the strategic national threats that can’t be tackled in isolation.”

Asked if he sees advantages for terrorism and organised crime fighting being led by the same organisation, Bristow said: “I can see advantages for shared capability.”

Bristow said NCA experts were also predicting a spike in heroin heading to the UK from Afghanistan after US forces pull out from the war-torn country later this year. Heroin from Afghanistan accounts for 90% of the class A drug on Britain’s streets: “We are predicting … that the availability and purity of Afghan heroin may well go up.” The director general is answerable directly to Theresa May – leading some in the police to suggest that in effect the NCA is a national police force directly under the control of government. But Bristow said he was not under government’s control, saying the home secretary had a democratic mandate to set the NCA’s priorities and budget, and he directed its operations.