A prioritisation list drawn up by health officials suggests routine testing would no longer be offered to swathes of the public, with tests restricted to hospital patients, care homes, certain key workers and schools.
It came as the UK recorded nearly 4,000 new Covid-19 cases in a day for the first time since the start of May, with a jump from 3,539 to 3,991 in one day.
On Wednesday, Boris Johnson said the Government was doing everything in its power to avoid a second national lockdown, which he said would be financially "disastrous" (see video below).
Ministers are poised to announce further localised measures, with pub curfews and a ban on households mixing across areas of the north-east from Friday.
Sunderland, Gateshead, Newcastle, Northumberland, South Tyneside and County Durham are set to go back into lockdown after a surge in cases. The restrictions will cover two million people.
Meanwhile, schools are drawing up plans to go part-time if the testing chaos continues, with headteachers warning that they will need to instigate rota systems in which pupils are taught on the basis of two weeks on and two weeks off unless the Government can get a grip on the testing system.
On Wednesday, Mr Johnson admitted for the first time that the testing system had "huge problems" trying to cope with a "colossal" spike in demand (watch the Prime Minister being questioned about testing in the Commons in the video below).
Despite rising cases, delays in releasing results saw the number of people getting a positive result the day after testing fall from 63 per cent at the start of the month to just eight per cent this week.
Ministers say the surge in demand for tests has been caused because too many people are seeking tests when they do not have symptoms or have not been contacted by NHS Test and Trace.
Officials say around a quarter of capacity is being used by those who do not meet current eligibility criteria. These include parents coming forward because their child is in the same class or year as a pupil with possible symptoms.
Matt Hancock, the Health Secretary (seen discussing testing problems in the video below), has said he is reluctant to introduce eligibility checks because he wants people with symptoms to get speedy access to tests, but Government sources said officials are considering limiting tests to the most high-risk groups if demand continues to outstrip supply.
A prioritisation list drawn up by health officials puts NHS patients, care home residents and frontline health and care workers at the head of the queue.
Those living in "watch list" areas – places assessed by the Government as having worrying levels of Covid-19 spread – would also be high on the list for tests. Schools, including teachers and pupils, are lower down, with ministers keen to avoid withdrawing tests from these groups.
At the bottom of the list lies the general public – in areas that are not suffering major coronavirus outbreaks (use the tool below to find out about cases in your area) – as well as businesses. Until now, ministers had suggested offering widespread testing to businesses could be used to get more people back to work.
A Government source said: "We are not yet at the stage of restricting access to tests for those people who have symptoms, and it is not something we want to do.
"Around a quarter of people who come for tests at the moment aren't eligible because they are asymptomatic so, before we do anything, we really want to deter this group.
"If we can do that while we are increasing capacity for tests we may not need to restrict tests for anyone with symptoms. But at the moment we are considering the options for what to do further down the road if it comes to that."
Key workers would be expected to bring proof of their role, such as a work pass.
On Wednesday, Mr Johnson said the Government was doing all it could to prevent a second national lockdown, telling MPs: "I think it would be completely wrong for this country and we are going to do everything in our power to prevent it. I very much doubt that the financial consequences would be anything but disastrous."
The Prime Minister said new restrictions including the "rule of six" (watch him announce the restriction in the video below) were necessary to "defeat" coronavirus.
He said on Wednesday night the only way to save family Christmases was to "be tough now" so the rule could be lifted before the festive period.
Mr Johnson admitted the current testing system had insufficient capacity to cope with demand. Asked about his ambition to roll out "moonshot" mass testing, the Prime Minister admitted the technology still appeared to be a "long way off", adding: "I'm going to be cautious and say that I can't sit here today and say we have such a pregnancy-style test."
Mr Johnson said that "in the case of schools, it's very important that teachers, parents, should look at the guidance... about when you should get a test," adding that whole classes and year groups should only be sent home if one pupil in the cohort tested positive and not on the basis of symptoms".
Headteachers warned on Wednesday that the situation was "unravelling". Geoff Barton, the general secretary of the Association of School and College Leaders, said thousands of pupils and teachers were now having to stay at home while they waited for tests.
"I think we will start to see rota systems bought in because there are teachers waiting for tests and they simply can't cover all the classes," Mr Barton said. "Schools will worry about whether in fact the only way to ensure you have sufficient teachers is to move to a rota. I am not trying to scaremonger, but this does appear to be unravelling."
Amid scenes of chaos, several Accident and Emergency departments issued pleas for the public to stay away after high numbers turned up seeking Covid-19 tests in Bolton, Liverpool and Plymouth.