The Tory MP and civil liberties campaigner David Davis MP said the measure to link subscribers’ data to particular smartphones, laptops or other devices through their internet protocol (IP) addresses was a practical change, but that it shouldn’t serve as a “stepping stone back to the old snooper’s charter”.

The brand new law may also allow the police to compel web firms to hand over data showing who’s using smartphone or a computer at any special time.

The Lib Dems also welcomed the move, saying Nick Clegg had repeatedly pressed the house secretary, Theresa May, to introduce propositions to match IP addresses with subscribers’ data since he blocked the introduction of the “snooper’s charter”.

“It’s good news that the Home Office has eventually got round to creating proposals on this after being repeatedly requested by Nick Clegg. This is just the type of matter that subscribers should take action on, instead of proposing an unworkable unnecessary and disproportionate snooper’s charter. There is completely no chance of that illiberal bill coming back under the coalition government. It is dead and buried.”

The draft communications data bill would have required internet service providers to store data monitoring users’ online activity for 12 months and allow it to be available to the police and security services.

The MPs and peers said the data would ensure it is possible to track who was using a specific IP address at a specified point of time.

Unique devices do not have their own IP addresses, but are assigned one each time they go online. The same addresses may be used by different devices at different times. As such, the police battle to demonstrate a specific individual, as well as a connection between something that’s occurred online, like accessing child abuse images.

Davis told The Andrew Marr Show on BBC1: “It’s a stepping stone back to the old snooper’s charter, the matter that parliament roundly threw out about a year and half ago, two years ago, because they were not convinced that this was crucial.

“Now this technical change is acceptable, it’s sensible, but the home secretary has said in effect that she views it as a route back into the entire snooper’s charter and, honestly, I think she is going to have real trouble.”

May confirmed the new conditions would be included in an anti- terrorism and security bill due to be published on Wednesday.

The legislation will also comprise David Cameron’s more contentious plans to ban British citizens who are identified as terror suspects from the state for up to two years, give authorities wider powers to seize the passports of suspected jihadis leaving the nation, and refuse landing rights in Britain to airlines that fail to provide passenger lists beforehand.

The bill also features developments to the terrorism prevention and investigation measures that are accustomed to monitor terror suspects in Britain, for example, introduction of a power to order a suspect to live in another part of the country. The threshold of proof required to exercise such measures will be raised, along with the bill will also confirm a more narrow definition of terrorism in a bid to make sure innocent individuals are not targeted by the brand new powers.