David Cameron has been warned not to reject a recommendation to strengthen the oversight of Britain's spies by stripping ministers of the power to sign off interception warrants.

The Government will draw up draft plans for new surveillance powers by the autumn with proposed laws put before Parliament early next year in response to a major report on the way the security agencies use communications data.

Terror laws watchdog David Anderson QC called for security services and police to keep intrusive powers to combat terrorism and serious crime but urged the Government to draw up "comprehensive and comprehensible" new legislation "from scratch".

A key recommendation would see the authority to sign off interception warrants, which allow agencies to view or listen to the content of a suspect's communications, transferred from ministers to judges in most cases.

Downing Street said the Government would consider all Mr Anderson's recommendations, including the proposal to give judges rather than ministers the authority to sign warrants, but stressed that the security services must remain able to respond quickly to threats.

But former minister David Davis said: " It is difficult to understand how the Prime Minister imagines that a system that requires the home secretary of the day to approve an average of 10 warrants every working day - and presumably many more on some days - is either effective or expeditious.

"Clearance of interception warrants are very serious matters, which take careful and well informed decision making. Security-cleared judges with many years of experience are more likely to be able to do this more quickly and effectively, and with greater impartiality, than any home secretary or other secretary of state.

"I know of no other civilised state which allows ministers to decide on such serious invasions of individual privacy without recourse to the courts.

"David Anderson describes the current law as 'variable in the protections it affords the innocent', and elsewhere as lacking in 'statutory safeguards'.

"Interception warrants is one area where that is certainly true, and Parliament will have to come to its own conclusion as to whether a system that relies on politicians rather than judges to approve surveillance and intercept is acceptable in a modern democracy."

Former attorney general Dominic Grieve said Mr Anderson makes a "very powerful case" that "to provide the necessary public reassurance in a new framework, involving the judiciary in this would be desirable".

He told BBC2's Newsnight: "In fairness to the Prime Minister, he has got to go away and provide a response. This is a report he commissioned and we then have to look at it and look at the issues.

"But the idea of having independent scrutiny of the warranty system so that the warrant is not just signed off by a politician seems to me to be a very desirable thing to do."

The Prime Minister's spokeswoman said Mr Cameron's view was "we need to consider that recommendation, along with others, fully".

She said: "The starting point when you look at any changes to a system has to be, 'what is this for?'.

"You do need to be able to respond quickly and effectively to threats of national security or serious crime."

Home Secretary Theresa May was urged by Mr Davis to ensure the transfer of powers from ministers to judges took place "as soon as possible" when she responded to Mr Anderson's report in the Commons.

She said: "It is important we recognise that question of the relationship between the executive and the judiciary is not just one that relates to the powers David Anderson has been looking at and we need to think very carefully about this particular issue."

Mrs May said she was "not in a position and do not intend to say the Government is going to do one thing or another".

"I think it is right we reflect more fully on these aspects and come with our proposals in the draft Bill we will publish in the autumn," she said.

More than 2,000 warrants for interception of data were issued last year.

Mr Anderson said: "Do we really want a home secretary who has to authorise 2,345 of these warrants in a year as well as managing a huge department of state?"

In his 372-page review, he said "bulk collection" of intercepted material must be allowed to continue - provided additional safeguards are introduced - citing a number of cases in which it had been used to thwart terror plots.

A "law-based system" must also be developed to cope with the emerging problem of encrypted services, it said, warning that "no-go areas" that cannot be accessed by intelligence services must be minimised.

Forcing technology firms to retain web browsing histories - a key plank of the controversial legislation labelled a "snooper's charter" by critics - may be "useful" but a "detailed operational case" must be made out, the review said.

Mr Anderson, the independent reviewer of terrorism legislation, was commissioned to carry out the review outside of his normal duties when the Government rushed through new laws to maintain existing capabilities last year.

The report, titled A Question Of Trust and containing more than 100 recommendations, concluded that the Regulation of Investigatory Powers Act, which was introduced 15 years ago to govern surveillance techniques, has been "patched up so many times as to make it incomprehensible to all but a tiny band of initiates".

It added: "A multitude of alternative powers, some of them with statutory safeguards, confuse the picture further.

"This state of affairs is undemocratic, unnecessary and - in the long run - intolerable."