"We don't have enough courts, we don't have enough judges, and we don't have enough police officers to tackle the real scale of illegal behaviour on the internet.
"What that means is increasingly we're going to have to look to technical solutions, we're going to have to look to the internet industry to help civil society deal with this really enormous problem the dark web has created," Mr Carr told the BBC.
"The police service is acutely aware of the large and growing problem of cybercrime and is actively working with police nationally and internationally along with the private sector in a bid to combat criminality on the web," says Deputy Assistant Commissioner Janet Williams, the lead on e-crime for the Association of Chief Police Officers.
Yet for all their efforts much of the illegal activity on the dark web remains beyond the reach of the police, and to some supporters of the dark web, its anonymity is its virtue.
They point to the protection it has offered to anti-government bloggers who spread the message of revolution during the Arab Spring.
And they argue that it continues to provide cover for dissidents who might otherwise face persecution in China.
For US student and dark web user David, it is about freedom of choice:
"Many people share the belief, myself included, that drugs should be legal and the dark web is that belief put into action."
You can listen to the full report on 5 live Investigates on Sunday, 5 February at 21:00 GMT on BBC 5 live.
Listen again via the 5 live website or by downloading the 5 live Investigates podcast.