Liberal Democrats and civil liberties campaigners have welcomed new measures requiring internet service providers to keep data that identifies online users, but said it must not be seen as a way of reviving the “snooper’s charter”.

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

The new law will also allow the police to force internet firms to hand over data showing who is using a computer or smartphone at any particular time.

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

“It is good news that the Home Office has finally got round to producing proposals on this after being repeatedly asked by Nick Clegg. This is exactly the kind of thing that we need to take action on, rather than proposing an unnecessary, unworkable and disproportionate snooper’s charter. There is absolutely no chance of that illiberal bill coming back under the coalition government. It’s dead and buried.”

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

The joint parliamentary committee that strongly criticised the “snooper’s charter” recommended linking subscribers’ data to IP addresses. The MPs and peers said the data would make it possible to trace who was using a particular IP address at a given point of time.

Individual 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 struggle to prove a link between something that has happened online, such as accessing child abuse images, and a particular individual.

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

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

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

The legislation will also include David Cameron’s more controversial plans to ban British citizens who are identified as terror suspects from the country for up to two years, give police wider powers to seize the passports of suspected jihadis leaving the country, and deny landing rights in Britain to airlines that fail to supply passenger lists in advance.

The bill also contains changes to the terrorism prevention and investigation measures that are used to monitor terror suspects in Britain, including the 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, and the bill will also establish a narrower definition of terrorism in an effort to ensure the new powers do not target innocent people.

May said the bill was needed to counter the “increased threat” Britain faces.

Asked on The Andrew Marr show whether the measure to link web users and their devices to IP addresses was a step back towards the snooper’s charter, she said: “This is a step but it doesn’t go all the way to ensuring that we can identify all the people we will need to … The National Crime Agency … will still not be able to identify everybody who is accessing illegal content on the internet.”