Labour is calling for a clear and fair “one nation deal” for English regions facing the toughest Covid restrictions.
The opposition has accused No 10 of a “divide and rule” approach to different parts of the country after talks with Greater Manchester ended acrimoniously.
Lisa Nandy said “playing” councils off against each other was unacceptable and a “national framework” was needed.
Ministers say a “consistent and fair” formula for future talks with other regions will be outlined on Thursday.
It comes as South Yorkshire announced it would enter the highest tier of Covid measures on Saturday.
Ministers have defended the level of financial support available to areas already in tier three, such as Liverpool City Region and Lancashire, in which pubs and bars not serving meals and other leisure businesses have to close.
They say their offer of £60m in overall business support to Greater Manchester – which was rejected by its Mayor Andy Burnham on Tuesday – was still on the table.
But Wigan MP Ms Nandy said the government was responsible for the “absolute mess” in Greater Manchester, accusing them of “shutting down the negotiations” after Mr Burnham held out for £65m.
She told BBC Radio 4’s Today that this was part of a pattern of behaviour in which local leaders across the North of England were “bullied” into accepting restrictions without adequate financial support.
“What we have got at the moment is the worst of all worlds where the government says it wants to take a local approach but when local areas stand up for what is needed for their communities the government say we don’t want to negotiate with you.”
Labour have tabled a motion for debate in the Commons later calling for “clear and fair” standardised criteria for Tier 3 negotiations, with more parts of the country expected to enter the highest category in the coming weeks.
The government is expected to win the non-binding vote, although it will indicate the level of disquiet on the Conservative benches about ministers’ handling of the situation.
Asked what Labour was proposing, Ms Nandy said keeping the current funding model used by the government – in which support is calculated per head of the population – was one option as long as it was better funded.
Another option, she said, was a “national scheme” of wage support based on the furlough scheme, which subsidised up to 80% of workers’ pay since March and which is due to expire at the end of the month.
She said the government needed to make good on its promise to support businesses and the self-employed through the winter, particularly in areas such as hers which had been living with restrictions for months.
“At the moment, it feels like the government is taking a divide and rule approach and playing us off one against one other which is really unhelpful,” she said.
“If you don’t provide financial support to one part of Greater Manchester, you don’t help any of us. That is how you do things in the North. That is what we asking them to do.”
The government’s new Job Support Scheme, which replaces the furlough programme, will pay up to two-thirds of wages of businesses forced to close.
Communities Secretary Robert Jenrick said the government would publish a “consistent and fair” formula for further support for local councils on Thursday.
“We’ve been very clear that it needs to be proportionate so that’s it fair to people,” he told Today, saying it would comprise cash for local contact tracing and business support.
“You can see that’s working out as 20-21% per head in Merseyside and Lancashire, I expect similar arrangements in South Yorkshire and other parts of the country. That’s what we offered to Andy Burnham.”
He appealed for local councils in Greater Manchester to come direct to him to make arrangements, saying that “the money is still there”, with “GM’s name on it”.