Chair of the Housing, Communities and Local Government committee and Sheffield South East MP Clive Betts raised concerns over the "level of cuts" faced by councils across the country.
He spoke of the "democratic accountability" challenge being faced when families were seeing their council tax rise while services were "cut" to finance social care.
Speaking during an Opposition day debate in the Commons on Local Government Finance, he said: "No other part of the public sector has had this level of cuts and we know as well that the biggest cuts have fallen to the poorest areas in the north of the country."
Mr Betts said it would be "interesting to see how the Government responds now" to the pressures on services in areas like South Yorkshire and the North East following December's General Election, adding: "Maybe they have a bigger interest in defending those areas in the future."
There were he said "massive pressures" on social care including children's services and services for the elderly.
He added: "We also know that in trying to prioritise spending on social services, council spending on social services has actually risen from 2000 to 2020 from 45 per cent of their total spending to 60 per cent.
"That has squeezed out spending for all other important services.
"So if you look at spending on things like road safety, on libraries, on leisure, on buses, on housing, on environmental services
"Things that are really important to the vast majority of our constituents, they've all been cut by 50 per cent or more."
Mr Betts warned there was a "challenge to the whole of our democratic accountability at local level, where people see their council tax rising...every year, yet they see that the services that most families receive, who don't get social care, those other services are being cut as they pay more for them. I think it's a real fundamental challenge that has to be addressed".
Mr Betts spoke of the need for a fair funding review for councils that was "genuinely fair", adding: "You can't have fair funding for local government unless the totality of the funding is sufficient for all councils."
He backed cross-party discussions to address social care funding, plus reform of council tax bands.
He said: "That is the challenge, how you devolve powers but also the ability to raise money in a country where the inequality is so great that raising money at local level means so much difference in the amount of money that can be raised from any individual tax."
Labour also warned councils in former Labour heartlands could run out of money under the Government's new funding plans.
Shadow Local Government secretary Andrew Gwynne said it was "not one nation" to redistribute money from the least well off areas to richer shire counties.
However, the Prime Minister rejected Labour's assessment, and in an amendment selected by the Speaker in his name, said his Government is investing "the biggest year-on-year real-terms increase in councils' spending power for a decade".
Mr Gywnne told MPs that councils in areas won by the Tories at the general election, Labour's former so-called "red wall", may not be able to meet their statutory duties as they would not have the funds to cover them.
He said: "Those councils who have the greatest social need, the worst health inequalities and with a limited tax base to make up for any financial losses, the so-called 'fair-funding formula' could be the factor that tips them over the edge."
He added: "To take money from some the poorest communities in the country to give it to the richest communities in the country with the ability to raise it (sufficiently) locally is not one nation."
Tory backbencher Steve Double, MP for St Austell and Newquay, said deprived communities do not exclusively live in Labour-run urban areas and many in his Cornwall constituency are less affluent.
He said: "Can I just gently say to him, not all deprivation is found in urban areas.
"And places like Cornwall that have had a raw deal of central Government funding because of the formula that has been put in place by the party opposite have for decades now received lower levels of funding despite being one of the poorest parts of England."
Mr Gwynne also warned that social care funding in former Labour constituencies could be hardest hit.
"Many of the areas that voted Conservative for the first time 2019, the so-called 'red wall' seats - areas that put their trust in the Government for the first time - will see some of the largest cuts to social care funding if the plans go ahead in the ways that have been outlined," said Mr Gwynne.
"Indeed, three quarters of those red wall constituencies, those seats that gave the Prime Minister his majority, will see millions of pounds of funding diverted from their hard-pressed councils to another part of the country."
Northern Powerhouse minister Jake Berry said the Government would "level up" communities across the country.
"As we entered a new decade, this country voted emphatically for a new government and a new approach," said Mr Berry.
"They discarded the politics of division and deadlock that had beset our last Parliament for so many years. It is the people who gave a new mandate to the Prime Minister to drive forward his vision for our nation.
"A vision that will see communities levelled up, opportunities spread equally over this country just as talent is already spread. We will level up every single nation of the United Kingdom, we will drive forward our Government's agenda."
Mr Berry also accused Labour of "scaremongering" by using Local Government Association figures to raise concerns about funding.
The minister said: "(Mr Gwynne) should think on before he scares some of the most vulnerable in society with stories about cuts which will not be based on a true formula."
Former Liberal Democrat leader Tim Farron said national parks, such as areas of the Lake District which he represents, have also suffered from local government cuts.
He said: "With that lack of an ability to rein in money of their own, those cuts are felt all the more keenly.