The security services will not be allowed to access web users' full browsing histories under new surveillance powers, Theresa May has insisted.

The Home Secretary said it was "simply wrong" to suggest that new powers in the draft Investigatory Powers Bill to access "internet connection records" would allow the collection of someone's full web history.

Mrs May said it would allow the likes of the police and GCHQ to know if someone has visited a social media website like Facebook - but not which pages they looked at, who they communicated with, or what they said.

Mrs May claimed the new powers allow access to "the modern equivalent of an itemised phone bill" and would not allow security services to see whether someone had visited, for example, a medical or news website.

Instead only "communications websites", illegal websites and certain IP addresses would fall under the scope of the plans.

The Home Secretary said there would be stricter safeguards in place for accessing the records over and above what is in place for current powers and that local authorities would be banned from using them.

In a Commons statement, she said: "Some have characterised this power as law enforcement having access to people's full web browsing histories.

"Let me be clear, this is simply wrong - an internet connection record is a record of the communications service that a person has used, not a record of every web page they have accessed.

"So if someone has visited a social media website, an internet connection record will only show that they accessed that site, not the particular pages they looked at or who they communicated with or what they said.

"it is simply the modern equivalent of an itemised phone bill.

"Law enforcement agencies would not be able to make a request for the purpose of determining, for example, whether someone had visited a mental health website, a medical website or even a news website.

"They would only be able to make a request for the purpose of determining whether someone had accessed a communications website, an illegal website or to resolve an IP address where it is necessary and proportionate to do so in the course of a specific investigation.

"Strict limits will apply to when and how that data can be accessed, over and above those safeguards that apply to other forms of communications data and we will ban local authorities from accessing such data."

Mrs May said the new power on record collection would end the "illogical" current position whereby suspects can be tracked on their mobile phones but not on social media or communications apps.

She said: "It cannot be right that today the police could find an abducted child if the suspects were using mobile phones to coordinate their crime, but if they were using social media or communications apps then they would be out of reach.

"Such an approach defies all logic and ignores the realities of of today's digital age."

Mrs May said the Bill also includes provisions for "equipment interference", meaning communications companies will be legally required to help spies hack into smartphones and computers.

It will allow bulk surveillance of the kind revealed in leaks by former US security contractor Edward Snowden as well as the ability to intercept the contents of online or telephone communication.

Existing powers allowing collection of so-called "metadata" - the who, what, where and when of a particular communication - are also included in the scope of the Bill.

The Home Secretary said it was a departure from the heavily criticised "snooper's charter" blocked by the Liberal Democrats during the coalition government and represented the security services' "licence to operate".

She said: "Today's Bill represents a significant departure from the proposals of the past.

"Today we are setting out a modern legal framework which brings together current powers in a clear and comprehensible way.

"A new Bill that provides some of the strongest protections and safeguards anywhere in the democratic world and an approach that sets new standards for openness, transparency and oversight."

Mrs May said the Government intends to ensure powers available to law enforcement, security and intelligence agencies are "clear for everyone to understand", with a transparency report published.

She said: "There remains some powers that successive governments have considered too sensitive to disclose for fear of revealing capabilities to those who mean us harm.

"I'm clear we must now reconcile this with our ambition to deliver greater openness and transparency. So the Bill makes explicit provision for all of the powers available to the security and intelligence agencies to acquire data in bulk.

"That will include not only bulk interception provided under the Regulation of Investigatory Powers Act, and which is vital to the work of GCHQ, but also the acquisition of bulk communications data both relating to the UK and overseas."

Mrs May said this is not a new power but will replace an existing one.

She confirmed a "double lock" approach to accessing communications information, with a judge required to approve a warrant signed by the Secretary of State.

Mrs May said: "This will be one of the strongest authorisation regimes anywhere in the world and for parliamentarians we will go even further."

She confirmed the Prime Minister would also be consulted when proposals to intercept the communications of MPs, peers, UK MEPs and politicians in the devolved legislatures are put forward.

Shadow home secretary Andy Burnham said it was important to stress the proposals are "neither a snoopers' charter nor a plan for mass surveillance".

The Labour frontbencher said the UK's laws are outdated given changes in technology, noting the jobs of the security services and police are harder.

Mr Burnham said: "In a world where the threats we face internationally and domestically are growing, Parliament cannot sit on its hands and leave blind spots where the authorities can't see."

He said strong powers must be balanced by strong protections for the public, adding: "What the Home Secretary has said today, it seems clear to me both she and the Government have been listening carefully to the concerns that were expressed about the original legislation presented in the last Parliament."

Mr Burnham added: "I think it would help the future conduct of this important public debate if this House sent out a unified message today that this is neither a snoopers' charter nor a plan for mass surveillance."

He questioned what data will be retained by the authorities, for how long and whether it will be held in anonymised form, noting public concern has risen following the hacking of TalkTalk.

Mr Burnham also asked how the law will apply to journalistic sources and questioned if the judicial oversight of warrants will delay action.

Looking at the wider context, Mr Burnham said: "There will be fears in some communities, particularly the Muslim community, that these powers will be used against them disproportionately."

He noted police powers have been wrongly used against trade unionists in the past.

Mr Burnham said the Opposition will examine the Bill carefully and seek to improve the safeguards, adding he believes Mrs May has "broadly got that difficult balance right".

Responding to Mr Burnham, the Home Secretary thanked her Labour shadow for the tone of his response.

But she was critical of attacks on the Prime Minister, telling MPs: "It was not justified by the rest of the tone of your speech.

"What we are saying is we want to work with people, mainstream voices in communities to help to encourage those mainstream voices and to work to encourage people when they are in isolated communities we identify the barriers that cause that isolation."

Mrs May said the Bill would only apply to "serious crimes" as already defined in legislation.

On encryption, she said: "We are not banning encryption - we recognise it plays an important part for people in keeping their details secure."

The Home Secretary said warrants issued in the UK on overseas providers should be exercised against that firm.

On journalistic sources, Mrs May added: "We will put into this legislation what we put into the Pace (Police and Criminal Evidence Act) code earlier this year - for access to communications data to identify a journalist's source, it will require judicial authorisation."

Former shadow home secretary David Davis said: "Will this replace all 66 statutory approval mechanisms for intercept and use of communications data?

"Will the judiciary who are involved in the authorisation procedures be appointed by the Judicial Appointments Commission or by the Prime Minister?

"And will MPs get the same protections on communications data that are now being extended to journalists? My understanding is that's not the case."

Mrs May said: "The process of interception where a warrant is currently required as signed by a secretary of state in future will have the double lock on it.

"There will also be additional processes which will be introduced in relation to some of the bulk capabilities that I referred to.

"Obviously we have to appoint the investigatory powers commissioner and there will be a process of determining who should be under that investigatory powers commissioner and the expertise they should have."

Former Liberal Democrat leader Nick Clegg said the proposals were "much improved" compared with the so-called snoopers' charter.

But he warned: "I have a feeling under the bonnet it still retains some of the flaws of its predecessor."

Mr Clegg said: "You have set out a somewhat complex double lock compromise which may incur stop-start delays. Would it not be simpler and faster to provide for direct judicial authorisation?"

He also queried why it was necessary to hold so much internet browsing data.

Mrs May replied: "I think very simply the double lock provides both judicial independence but also crucially public accountability."

Home Affairs Select Committee chairman Keith Vaz said he was worried that the internet records powers may allow more data to be collected than Mrs May was implying.

He said: "I know you said the information is equivalent to an itemised bill but there's a lot of information in an itemised bill.

"If I were to look at your itemised telephone bill and you were to look at mine we might be surprised at who we were telephoning."

But he welcomed Mrs May "ripping up" old and unfit for purpose legislation and the ban on local authorities accessing information about their own citizens.

The Labour MP said he was concerned about who would train the panel of judges providing oversight.

Replying, Mrs May stressed judges are used to making independent decisions on judicial reviews and said she had faith they would act independently.

Justice Select Committee chairman Bob Neill agreed that faith should be put in the judiciary but stressed that a judge needs to be on call for 24 hours a day to authorise warrants.

He said: "Can you ensure, for example, that an appropriate senior judge is available to be on call on a 24-hour basis as is perfectly common in other types of judicial review proceedings so that delay is minimised?

"Will you also give us more detail as to how the appointment of the judicial commissioners is to take place and who will be responsible for that?"

Mrs May said discussions have already taken place with the judiciary which would continue and take into account Mr Neill's concerns.

Former shadow home secretary Yvette Cooper welcomed judicial authorisation and the commitment to transparency but asked whether the new Investigatory Powers Commissioner would be accountable to the Government or Parliament.

The Labour MP said: "It sounds like something we have called for but will it be accountable to the executive and to the Prime Minister, which has limited the operation of some of the existing commissioners, or will it instead be accountable to Parliament or to the ISC?

"And how will it interact with the existing counter terror reviewer because I do think David Anderson has done an extremely good job in that role."

Mrs May said the commissioner will be appointed by the Prime Minister and will regularly publish public reports and recommendations.