Council workers are being sent to knock on the doors of potential coronavirus sufferers who fail to answer the phone amid increasing frustration with the NHS Test and Trace system.
On Tuesday, Simon Clarke, the minister for regional growth and local government, said talks were ongoing about the best way to increase the proportion of positive cases and their contacts being reached by the service.
It followed warnings that reopening schools without an improvement in test and trace performance could cause a second wave of coronavirus twice the size of the first one.
Mr Clarke said the Government was now looking at whether "there should be some physical follow-up if you can't reach [potential cases] on the phone".
But councils in areas subject to partial lockdown are already sending staff out amid concern that the national programme is missing too many cases.
In Blackburn with Darwen, Lancashire, where the infection rate is 10 times that of England's average, council teams will now track down anyone who cannot be reached by the national system after 48 hours.
If phone calls cannot reach those identified as positive cases, or contacts of them, then council workers will visit their addresses in order to deliver advice to self isolate.
Dominic Harrison, Blackburn with Darwen council's director of public health, said: "We are now developing our own local contact tracing system. The national system is simply not tracing enough cases and contacts fast enough."
The Department of Health and Social Care said it was working closely with local authorities and had "assigned a ring-fenced group of NHS contact tracers to follow up positive cases" in Blackburn with Darwen. Council workers are assigned to knock on doors in cases where such efforts fail.
Officials in Greater Manchester are understood to be considering taking similar steps.
During its lockdown, Leicester introduced door-to-door testing because of anxiety that too few people were coming forward for tests.
Sandwell Council, in the West Midlands, last week became the first local authority to set up its own system after its public health director, Lisa McNally, said the national system was failing.
She said the council was contacting cases as soon as they came in, rather than "waiting for test and trace to fail to reach them".
Under the NHS Test and Trace programme, call handlers aim to make contact with all infected people and their contacts to advise them to self-isolate. But if they cannot make contact after 10 calls, they are advised to move on to the next case.
The Scientific Advisory Group for Emergencies (Sage) has said Test and Trace needs to reach at least 80 per cent of contacts of positive cases within 48 hours to be effective.
Currently, roughly 80 per cent of those who test positive are reached by contact tracers, with around the same proportion handing over details of contacts. Of those, around three quarters of contacts are reached – equating to overall coverage of 50 per cent.
The moves by local councils reflects growing frustration among local health officials with the national test and trace system, launched in May.
The NHS system, run by the former TalkTalk executive Dido Harding, involves more than 20,000 contact tracers employed by private firms such as Serco and Sitel.
Government minister Mr Clarke (see video above) defended the system's record but signalled that officials may play an increasing role knocking on doors.
He said: "We need to keep driving those numbers up and we are constantly working out for example the best time of day to call people to try and reach them. We're looking at whether there should be some physical follow up if you can't reach them on the phone."
The shadow health secretary, Jonathan Ashworth, said: "Boris Johnson is handing multi-million pound contacts to firms like Serco and claiming his approach is 'world-beating' when it is far from that and showing no signs of improvement. He should be honest with the public about his Government's failings.
"Given that infection rates are rising and some areas have had restrictions tightened, it is no wonder local authorities are abandoning Johnson's failed approach and setting up their own systems."
A Government spokesman said: "Our priority is to curb the spread of this virus and save lives, and local action to tackle outbreaks and keep people safe is a crucial part of the national NHS Test and Trace service.
"We continue to work closely with all local authorities and are providing targeted, additional support where needed, including in Blackburn with Darwen where we have assigned a ring-fenced group of NHS contact tracers to follow up positive cases."
Ministers have one month to fix the broken system and halt a devastating second wave of coronavirus or Britain will face a “long and bleak winter”, Sir Keir Starmer said.
The Labour leader told The Guardian there was “precious little evidence” of serious preparation for a resurgence in cases as he called for mass testing of asymptomatic people.