Rishi Sunak has been urged to rethink the allocation of cash for the government’s levelling up agenda after it emerged that his own constituency and Tory MPs’ seats are being prioritised.

Sheffield City Region mayor Dan Jarvis said that post-Covid it was “vital” that people feel government cash is allocated “on the basis of need, not political considerations”, while Labour leader Keir Starmer said “it feels like pork barrel politics”.

Documents published alongside the Budget showed that relatively well-off Richmondshire, which is represented by the chancellor, was prioritised for money from the £4.8bn levelling up fund, despite it being among the less deprived areas of the country.

Meanwhile, the vast majority of areas – 40 out of 45 – given a share of the separate £1bn towns fund are represented by Conservative MPs, which Jarvis said was “an imbalance so marked it is impossible to believe it coincidental”.

Turning to the levelling up fund, the mayor questioned why Richmondshire (251st out of 317 on the deprivation index) was given category one status and therefore preference for funding, over Sheffield (93rd on the deprivation index) and nearby Barnsley (38th), which are both in category two.

Areas like Salford (20th) and Halton (39th) were also placed in category two, Jarvis said in a letter to Sunak.

He also pointed out that Richmondshire, in North Yorkshire, has suffered 141 Covid deaths per 100,000 people, compared to 311 in Barnsley and 188 in Sheffield, both in South Yorkshire.

Treasury sources said Sunak had no sight of the specific areas that would be deemed high priority for the levelling up fund, although ministers were able to see a provisional map showing how the cash would be spread under the categories.

Jarvis urged the chancellor to immediately publish the formula used by the government to decide which areas were given priority for cash.

“But whatever the exact formula, the practical reality is that you have allocated support in a way that favours places that are affluent over those that are deprived,” Jarvis wrote to Sunak.

“Places that are resilient over those that are vulnerable, places that have suffered less from Covid over those that have suffered more. 

“Poorer communities across the north have been treated especially unfairly, making a mockery of the government’s commitment to levelling up.”

He added: “At such a critical moment for our divided country, when families and businesses across the country need investment and support, we cannot afford to get this wrong. 

“I hope you will look again at these decisions.”

Jarvis argued that the allocations were part of a “wider pattern” where disadvantaged communities have been disproportionately affected by Covid, “but government support has not”.

He urged Sunak to demonstrate that the allocation of cash was not a repeat of the 2019 towns fund, which the Commons public accounts committee said was “not impartial” and had “every appearance of having been politically motivated”.

Jarvis told reporters: “It beggars belief that the chancellor’s relatively affluent Richmond constituency is considered to be in greater need of levelling up investment than Barnsley and Sheffield.

“It’s yet again proof that this government’s actions are levelling South Yorkshire down – pushing our region and some of the poorest places in the north to the back of the queue for investment.

“I’m pushing the chancellor and the Treasury to publish the allocation formula immediately. They must dispel any notion that this is a repeat of the towns fund fiasco.”

Earlier, Starmer said: “If we look at the towns fund there are 45 areas and 40 of those areas are where there is a Conservative MP.

“I think lots of people would scratch their heads and say: ‘What is going on here?’.

“This should be going where it is really needed and the government needs to publish the criteria for this because 40 of the 45 going to Conservative areas, this feels like pork barrel politics.”

The funding comes ahead of local elections in May and follows the Tory landslide of 2019 which saw a “red wall” of Labour-supporting seats in towns in northern England tumble in favour of Boris Johnson’s party.

On a visit to Teesport, Middlesbrough, on Thursday, the prime minister said: “I think if you look at the map, one of the functions of the election is clearly that there are a lot of Conservative-represented towns – I think that is just a basic electoral fact.

“I’ve asked about this and I’m told that the criteria was entirely objective – it takes in data on poverty, employment and so on.

“We want to unite and level-up across the whole country and want to do it in a completely impartial way, so that’s what we are doing.”