Official impact assessments on the emergency surveillance bill due to be rushed through parliament this week appear to confirm privacy campaigners' fears that the law contains sweeping new surveillance powers that will affect every man, woman and child in Britain.

Two Home Office impact assessments deposited in the House of Commons library late on Friday show that the legislation would add an extra £8.4m to the average annual bill for state surveillance. The figure covers the cost of extra payments to internet and phone companies for storing extra data and new safeguards to be put in place, such as a role for the information commissioner in overseeing data requests.

But more worryingly for privacy campaigners, the impact assessments make explicit that the legislation would confirm powers for the British government to impose sanctions and penalties on overseas internet and phone companies anywhere in the world that refuse to comply with an interception warrant from London to hand over the content of communications. The prime minister has insisted the fast-track legislation will do no more than confirm existing surveillance powers and put them beyond legal doubt.

The impact assessment on a section on enforcement of the new powers says the Regulation of Investigatory Powers Act 2000 (Ripa) imposes penalties on companies that refuse to comply with interception warrants and sets out the circumstances in which they may be requested to maintain permanent interception capability.

However, it is possible that a company may refuse to comply with a notice requesting it to maintain a permanent interception capability. In the event that an overseas company refuses to comply with such a notice, there is an established process for applying to a UK court via civil proceedings for an injunction to enforce compliance.

The Home Office adds that there is a process for enforcing overseas the decisions of UK courts and says the emergency legislation amends Ripa to make clear that companies can be obliged to provide assistance in relation to interception warrants.

The Home Office says the fast-track data retention and investigatory powers bill – known as the Drip bill – is not intended to extend the UK's reach around the world. Rather, it is to confirm that Ripa obligations in relation to interception apply to all companies providing services to people in the UK, irrespective of where they are based. This will maintain the ability of law enforcement and intelligence agencies to intercept the communications of those who would do us harm, says the official impact assessment.

The proposed legislation would not impose any new obligations on UK business. Instead, it is intended to put beyond doubt the obligations that already apply to overseas providers, it adds.

But privacy campaigners warn that these powers to pay companies anywhere in the world for helping British snooping efforts and sanctioning those who refuse to comply amount to new and unprecedented powers.

Isabella Sankey, Liberty's policy director, told MPs in a briefing being circulated on Sunday: "Clause 4 of the bill also contains new and unprecedented powers for the UK to require overseas companies to comply with interception warrants and communications data acquisition requests and build interception capabilities into their products and infrastructure. These provisions will expand existing mass interception powers that are due to be challenged in the British courts next week."

Privacy campaigners also fear that these extra-territorial powers could provide the legal basis for enabling a number of Tempora-style programmes around the globe. Documents leaked by Edward Snowden disclosed that GCHQ has been tapping into transatlantic fibre-optic cables and storing huge amounts of data for up to 30 days under its Tempora programme.

A joint briefing note to MPs by Liberty, Privacy International, the Open Rights Group, Article 19, Big Brother Watch and English Pen warns that the small print in clause 5 of the six-clause bill extends the 2000 definition of telecommunications services to enable a much wider range of data, including webmail and some social media traffic data, to be collected.

The privacy campaigners warn that the two clauses taken together mean that elements of the rejected snooper's charter are present in the emergency legislation.

They are pressing MPs and peers to ensure that the bill's sunset clause – the date the legislation automatically expires – is brought forward from December 2016 to this December. Sankey tells them: "This fast-track legislation contains sweeping surveillance powers that will affect every man, woman and child in the UK."