David Cameron was accused on Thursday by a radio presenter in Liverpool of being “so out of touch it’s untrue” about the impact of government austerity measures on the city.

Liverpool’s mayor has claimed that it could be bankrupt in two years because of funding cuts and forced to withdraw social care from thousands of elderly and vulnerable people.

The Prime Minister was challenged by Roger Phillips of BBC Radio Merseyside to spend a week in Liverpool and visit a food bank.

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The fractious exchanges came after Mr Cameron insisted the city was being treated fairly over the allocation of money to local authorities.

During the interview, he denied suggestions it was being harder hit than more prosperous areas, such as his Oxfordshire constituency, and said he was proud to lead a government that “generously supports areas with greater needs”.

Mr Phillips told him: “We get call after call after call from people saying you and your Cabinet are just so out of touch it’s untrue, you need to come up here and spend a week up here, work in a foodbank, find out what’s really, really going on at grassroots level and then you will understand why we feel perhaps we are being treated unfairly.”

Mr Cameron sidestepped the invitation and accused the media of distorting the extent of the cuts. He said: “One of the reasons people feel treated unfairly is because they hear on programmes like yours, day after day, week after week, sets of figures that aren’t accurate or right.”

As he insisted the entire country was “in it together” over austerity, Mr Phillips interjected: “Oh come on…”

The broadcaster said Liverpool was not feeling the effects of any recovery in London. Mr Cameron countered by pointing to jobs being created in the North West of England.

He said civic leaders were complaining about reductions to funding while building up reserves and failing to collect council tax arrears.

The Conservatives have long faced a difficult relationship with the voters of Liverpool, although their support is stronger in surrounding areas such as the Wirral.

Ten years ago Boris Johnson, the Mayor of London, apologised to the city after the Spectator magazine, which he then edited, claimed that Liverpudlians “wallow” in their “victim status”.