The home secretary, Theresa May, has made further concessions on the snooper’s charter, including on the key issue of privacy, before a Commons battle over the bill next week.

The concessions, intended to meet concerns raised by the parliamentary intelligence and security committee (ISC) as well as by Labour, Liberal Democrat and backbench Tory critics, include the introduction of a privacy clause designed to ensure that the new mass surveillance powers are not authorised in situations where less intrusive means could be used.

The two-day Commons report stage of the investigatory powers bill, which will extend the powers of the security services, is scheduled for Monday and Tuesday next week. It will be the last substantive piece of parliamentary business before the EU referendum in three weeks’ time.

The home secretary’s concessions also cover protection for journalists, the Wilson doctrine on shielding MPs from snooping, and the retention and use of “bulk personal datasets” such as medical records.

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The ISC, chaired by the former Conservative attorney general Dominic Grieve, and parliament’s joint human rights committee, chaired by the former Labour cabinet minister Harriet Harman, have also tabled amendments to the bill demanding much tougher safeguards preventing the powers from being abused.

The ISC in particular demanded that privacy protections should be made an overarching part of the bill.

The bill not only enshrines in law the bulk data collection and mass computer and phone-hacking operations carried out by GCHQ, which were revealed by the whistleblower Edward Snowden in 2013, but also extends the security services’ powers to track everyone’s web history by introducing internet connection records that can be stored for 12 months and that can be accessed by the police and security services.

The new Home Office concessions include:

• Privacy: a new clause that makes clear that warrants and other authorisations should not be granted where the information could reasonably be obtained by less intrusive means. The clause makes explicit the implicit privacy safeguards in the bill and puts “beyond doubt” that there will be severe penalties for those who deliberately misuse the powers.

• Protection for journalists: clarification that the judicial commissioner will be required to consider ‘the overriding public interest’ when authorising the use of communications data to identify a journalist’s sources.

• Wilson doctrine: prime minister must give explicit approval for law enforcement agencies to hack into MPs’ phones and computer as well as to access their communications data.

• Bulk personal datasets and medical records: the legal test needed to retain and examine these highly personal records is to be raised to “exceptional and compelling” cases only.

A Home Office spokesperson said: “We have always been clear that we will listen to the constructive views of politicians from all sides of the House to ensure the passage of this important bill. We have said the government will be bringing forward amendments at report stage and are willing to consider amendments that are in the interest of both improving the bill and of demonstrating the necessity of the powers it contains.”

Labour has already secured from May a commitment to an independent review of the operational case for bulk personal data collection and hacking powers by Britain’s watchdog on terrorism laws, David Anderson, and protection from surveillance for legitimate trade union activities.

However, Labour intends to press for further changes, including stronger safeguards in five areas: privacy, using internet connection records only in serious crime cases, toughening rules on the judicial authorisation of intercept warrants, stronger safeguards on the use of medical records and other bulk datasets, and protections for legal and journalistic confidentiality.

The Liberal Democrats, who could prove influential when the bill reaches the Lords, have tabled amendments that would remove “internet connection records” – tracking everyone’s web use – from the bill and that would ensure that people who are the targets of unlawful surveillance are told what data of theirs has been accessed so they can seek redress.

The Liberal Democrats’ home affairs spokesman, Alistair Carmichael, said the ISC told May to go away and rewrite the bill to include a dedicated section on privacy: “Instead she re-labelled the title ‘General Protections’ to ‘General Privacy Protections’, a one-word aesthetic addition that fools no one. That is why the Liberal Democrats will continue to fight, both in the Commons and Lords, for privacy to form the backbone of this legislation.

“Theresa May’s concession allowing for an independent review into bulk powers is welcome but this goes nowhere near far enough. Too many of the proposals in the bill are vaguely drafted and disproportionate; for example, we are clear that proposals to collect and store everyone’s web histories for 12 months has to go. We should be equipping our police and security services with the resources they need, not drowning them in data,” he said.

A report by the parliamentary joint human rights committee published on Thursday welcomes the “direction of travel” in the bill but proposes further safeguards.

The committee’s chair, Harriet Harman, said: “The bill provides a clear and transparent basis for powers already in use by the security and intelligence services, but there need to be further safeguards.

“Protection for MPs’ communications from unjustified interference is vital, as it is for confidential communications between lawyers and clients, and for journalists’ sources. The bill must provide tougher safeguards to ensure that the government cannot abuse its powers to undermine parliament’s ability to hold the government to account.”