In a concession to privacy groups, May said there would be jail penalties for anyone abusing the system and a two-tier oversight system with senior judges with veto power reviewing all the 2,800-odd ministerial-approved warrants issued each year to allow suspects' emails and conversations to be intercepted.

Amnesty International said the powers would "take the UK closer to becoming a surveillance state" and Shami Chakrabarti, director of civil liberties group Liberty, said the bill constituted "a breath-taking attack on the Internet security of every man, woman and child".

The opposition Labour Party broadly supports the bill, but veteran Labour lawmaker David Winnick said if the proposals were passed without substantial amendments "it would be very unfortunate and a bitter blow for civil liberties".

"I remain concerned, even if I am one of the few who do remain concerned, about the excessive powers which will be given to the security authorities in addition to what they already have, though judicial involvement is better than no judicial involvement," he told parliament.

Ministers and officials have argued that current British laws governing surveillance powers are outdated, drafted in the days before anyone anticipated the widespread use of social media, leaving the police and security agencies unable to keep up with technology used by terrorists and serious criminals.

In April last year, the European Court of Justice (ECJ) struck down an EU directive requiring telecoms companies to store communications data for up to two years because it interfered with people's right to privacy.

Britain rushed through emergency legislation as a result, but these measures were later ruled unlawful by London's High Court, meaning the government must produce a replacement by the end of next year.

After Snowden's disclosures, three major reviews cleared British spies of acting illegally but all agreed the laws needed an overhaul.

In unprecedented display, spy chiefs have invited journalists into their headquarters to argue for new powers and to try to reassure sceptics that they were not interested in mass state surveillance of people's private lives.

They have also pointed out that private companies such as Google or Facebook hold more data about individuals with less oversight.