The building was previously not on the DWP list of potential transition sites and so staff were caught unawares at the announcement, which is to impact just under 200 employees.
The letter, penned by Dame Rosie and Ed Miliband, raises concerns that the necessary impact assessments were not made for Doncaster Crossgate House.
The letter notes that Sheffield Hartshead Square is over 20 miles from the current site, meaning some staff might be unable to make the transition.
The letter also makes the point that removing these hundreds of jobs from the Doncaster area will have a negative impact on the local economy, contrary to the Government’s Levelling-Up agenda.
Said Dame Rosie: “It is deeply concerning that workers at Doncaster Crossgate House were given so little notice of their office’s closure.
"The Department for Work and Pensions had not previously listed Crossgate House amongst their potential sites to be moved, leaving employees feeling as though the rug had been pulled from under them.
“Many of the workers have told me about their positive experience working at Crossgate House, with some of them having been employed there for decades.
"This decision, which will take well over 100 jobs out of the area, will have a significant impact on Doncaster’s local economy at a time when the Government is meant to be
Ed Miliband added: “With 200 jobs moved out of Doncaster, this decision flies in the face of all the government rhetoric about levelling up.
"Moving these jobs to Sheffield will reduce employment and damage the economy in our town centre.
“I have been contacted by constituents deeply concerned about what it will mean for them with significant extra costs and time of travelling.
“They have also informed me that insult was added to injury with some staff hearing the news through the media rather than being told directly."
A government spokesperson said: “As part of plans to improve the services we deliver to claimants, help more people into employment and modernise public services, DWP is moving some back office staff to better, greener offices, which will not affect any public-facing roles.
“This is not a plan to reduce our headcount – where possible, our colleagues in offices due to close are being offered opportunities to be redeployed to a nearby site, or retrained into a new role in DWP or another government department. We are making every effort to fully support our staff through this process.”