The bill, to be unveiled in Parliament on Tuesday, pulls together many measures set out in Labour’s general election manifesto.

But they come amid questions over whether police have the money to make the government’s plan work.

Under the bill, police would gain the power to enter and search a property without a court warrant for a stolen mobile phone or other items that have been electronically tracked, such as laptops or Bluetooth-tagged bikes.

The power would mean that victims of mobile phone thefts, who are tracking their device while it is in the hands of a criminal, could call on police to recover it quickly.

Cooper told BBC Radio 4’s Today programme she understood the “incredible frustration” of phone theft victims who say “I can track it, I can see where it is – it’s in this particular house, it’s in this particular location”.

“And yet the police can’t act fast enough to be able to track it down,” she added.

Cooper said “we have to have the stronger powers and action [and] the police say they welcome this”.

Asked about the reliability of locator apps, where people can use another device to help track down the location of their missing or stolen phone, being used in police searches, Cooper told BBC Breakfast: “Police will have to make decisions [and] it will need to be signed off by a police inspector, and [they will] need to make decisions about where the evidence is good enough for them to be able to act.”

She added that the bill would include scrapping a “ludicrous” £200 threshold for shoplifting, which meant lower value thefts were not currently prioritised by police.