The Department for Health is drawing up plans to relax lockdown rules for people living in Tier 3 areas, if they test negative for coronavirus.
People who have two negative tests would be allowed to follow the same rules as those in Tier 2 areas.
A Department for Health document prepared for local councils states: "Work is under way to rapidly assess options in this space, including the potential to allow the relaxation of Tier 3 restrictions down to those normally at Tier 2 for a time limited period for those who have two negative test results."
People who benefit from the scheme could be allowed to visit friends and family in groups of six outdoors, visit venues such as restaurants (if they can find any that are open) or attend live sporting events.
The aim is to encourage people to take part in a mass "community testing" programme, which the Government is keen to extend to Tier 3 areas such as the North East following the success of a scheme in Liverpool.
While Covid-19 tests are usually offered to people with symptoms, the community testing scheme involves testing large parts of the population whether they have symptoms or not.
Local authorities are free to propose whether they want people who are tested to receive extra freedoms, or not. But the Department of Health says it is "keen" to consider ways that restrictions could be relaxed.
A "prospectus" for local councils drawn up by the Department for Health states: "We are keen to explore ways we could potentially relax restrictions on a limited basis for those that test negative, but there will, rightly, be limits to what can be responsibly done."
It continues: "Although we will need to look at each proposal on its own merits, a national regulatory framework will be required to support such activities.
"Work is under way to rapidly assess options in this space, including the potential to allow the relaxation of Tier 3 restrictions down to those normally at Tier 2 for a time limited period for those who have two negative test results.
"For example, the ability to meet friends and family in groups of six outdoors, the ability to visit venues (such as hospitality venues, indoor entertainment, accommodation) which are otherwise closed at Tier 3, and/or the ability to attend large events (such as elite sport, live performances).
"As local areas develop their plans for community testing, we are very interested in discussing with them the full range of their ambitions in this space and will provide all necessary support to determine what would be a safe, responsible and workable approach within any future regulatory framework."
The document also says councils could choose to follow Liverpool's example and test the whole population, or to offer tests to only parts of it.
This could mean testing people in a specific geographic area where infection rates are high, with the entire local population being tested every three days.
Other possibilities suggested by the Department of Health include testing people over a certain age, or testing all school pupils, parents and staff twice a week.
Speaking at a Downing Street press conference on Monday, Health Secretary Matt Hancock said mass testing in Liverpool had helped move the whole city down to Tier 2.
He said: "In Liverpool, where over 300,000 people – both with symptoms and without – where that testing has happened, they’ve managed to bring the case rates down by over three-quarters.
"And so on Wednesday Liverpool will go into Tier 2, not Tier 3.
"Of course, I want to see this sort of success right across the board so we’re rolling out community testing much more widely.
"We’ve been working with those areas going into Tier 3 with colleagues in Scotland, Wales and Northern Ireland too.
"And today – with the publication of our community testing prospectus – we set out the next phase of that work to give Tier 3 areas a faster way out of the toughest restrictions, to support them to come down the tiers – as has happened in Liverpool.
"We’ve already received significant interest from around the country, including from the West Midlands, Redcar, Warwickshire and Medway and others."