Twenty Conservative MPs- including some from across Norfolk and Suffolk - whose constituents are currently under the lowest level of restrictions, have written an open letter to Mr Burnham and the Labour leader urging them to get the virus “under control” in Manchester to avoid the “pain” of a national lockdown.
Led by Jerome Mayhew, the MP for Broadland in Norfolk, they said: “We know you are calling for a national lockdown now but urge you to reconsider.”
They highlighted coronavirus rates that show some of their areas having rates far lower than Manchester’s.
“Given this disparity, it does not make sense to shut down the whole country when the virus is spiking in particular locations,” the MPs continued.
“It is very clear to us – and the people we represent – that the local and regional approach is the right response to the current situation.
“We urge you to work with the government to get the virus under control in Greater Manchester, so we can all avoid the pain of another national lockdown.”
Speaking on the BBC's The Andrew Marr Show on Sunday morning, the Greater Manchester mayor said: "I'm not sure a sort of 'we're alright Jack' letter from a group of southern Conservative MPs is going to cut much ice here.
"I would say to them some of them represent constituencies whose cases were higher than ours when we went into national lockdown.
"Anywhere could end up in Tier 3 this winter. In fact, I would say places are likely to end up in Tier 3 this winter, therefore it's everyone's concern that we protect the lowest paid in our communities."
The letter has also been attacked by Conservative MPs as being “very ill judged”.
As well as calling for more support for businesses forced to close under the tougher measures - Mr Burnham has threatened legal action - the mayor, along with Labour leader Sir Keir Starmer, is instead calling for a short national lockdown, arguing it would be fairer and would get his constituents’ greater support.
Senior Conservative William Wragg, whose Hazel Grove constituency is in Greater Manchester, recommended his colleagues “concern themselves with their own constituencies”.
“I would not wish tighter restrictions on their constituents,” he said.
“We’re willing to work constructively to improve the situation in Greater Manchester & would ask for the short time and space to do so.”
Christian Wakeford, the Tory MP for nearby Bury South, said politicians in the region were “united in opposing Tier 3 in its current form” in order to get the “best solution” for residents.
“Interventions from fellow members who don’t understand the situation are neither wanted nor helpful,” he added.