Three Cumbrian MPs have written to the prime minister calling for her to come up with £278m for Cumbria to match the £1bn deal for Northern Ireland under the negotiations with Democratic Unionist Party.

Barrow and Furness MP John Woodcock, Westmorland and Lonsdale MP Tim Farron and Workington MP Sue Hayman have penned Theresa May a letter urging her to invest in Cumbria following an agreement of an additional £1bn of public sending in Northern Ireland over the next two years.

Political leaders in Scotland and Wales reacted furiously to the deal, which will see Northern Ireland benefit from additional cash while Mrs May will gain the support of DUP MPs in crucial votes at Westminster. Welsh First Minister Carwyn Jones described it as a "straight bung'' to prop up a ''faltering'' Conservative minority government, while his Scottish counterpart Nicola Sturgeon tweeted: "Any sense of fairness sacrificed on the altar of grubby DUP deal to let PM cling to power."

The Cumbrian MPs said they accept Northern Ireland has a case to be made for greater spending due to "historic under-investment and special geographical circumstances", but said "a similar case" could be made for many areas of the UK "including Cumbria".

In the letter to Mrs May, the MPs wrote: "You will be aware that for many years Cumbria has suffered a relative under-investment in infrastructure which has accentuated the difficulties caused by the unique geography of the county. This problem has only been exacerbated by Cumbria’s omission from the Northern Powerhouse project.

"Given the challenges we face, we are struggling to explain to our constituents why the government feels it is a priority to spend huge sums of money on roads, rail and broadband in Northern Ireland whist the same issues go unaddressed in Cumbria.

"By our calculations the extra spending per head of population in Northern Ireland would result in an additional £278m of investment in Cumbria over the next few years. This is in addition to the money that we expect Cumbria will receive as part of the UK shared prosperity fund as we exit the European Union.

"Please can you provide details of when such money might be forthcoming so that we can reassure our constituents that they have a government which allocates investment in a fair way across the United Kingdom?"

Mr Woodcock said: “The government have been telling us for years that there is no money to invest in Cumbria, and yet they have found £1bn for Northern Ireland in order to cling on to power.

“The need for investment in roads, rail and broadband in Cumbria is just as great as in Northern Ireland and I know people will want to know on what basis the government has found cash for her new friends in the DUP but not for us.

“We are asking Theresa May to come up with £278m for Cumbria to match the £1bn she has found for Northern Ireland to prove that her government is committed to spreading prosperity across the whole of our country.

“If the calls made by the county's Conservatives to fight for investment in Cumbria are genuine, I am sure they will want to join us in lobbying for this."