David Cameron has been accused of breaching the ministerial code after writing to his local council criticising service cuts and offering help from Downing Street advisers.
The Prime Minister wrote to Ian Hudspeth, leader of Oxfordshire Council, in his capacity as MP for Witney expressing "disappointment" at the way savings were being achieved.
Labour has demanded a probe by the Cabinet Secretary over whether Mr Cameron broke the rules by offering to use No 10 staff to benefit the constituency.
In the exchange of letters with Mr Hudspeth, obtained by the Oxford Mail newspaper, Mr Cameron wrote: "I was disappointed at the long list of suggestions floated in the briefing note to make significant cuts to frontline services - from elderly day centres to libraries to museums.
"This is in addition to the unwelcome and counter-productive proposals to close children's centres across the county.
"I would have hoped that Oxfordshire would instead be following the best practice of Conservative councils from across the country in making back office savings and protecting the front line.
"In that context, I would be happy to initiate a further dialogue with individuals in the Number 10 Policy Unit and yourself. Please contact Sheridan Westlake (address) if you wish to take this up."
Mr Hudspeth replied that the council had already cut its back office functions, looked at shared services, reduced staff numbers by thousands and disposed of property.
He pointed out new functions that had transferred to the council, including public health and social care.
"Excluding schools, our total government grants have fallen from £194m in 2009/10 to £122m a year in 2015/16, and are projected to keep falling at a similar rate," he said. "I cannot accept your description of a drop in funding of £72m or 37% as a 'slight fall'."
Mr Hudspeth also said he had "worked hard to assist you in achieving a Conservative majority".
Shadow Cabinet Office minister Jonathan Ashworth has written to Cabinet Secretary Sir Jeremy Heywood asking for a ruling on whether the ministerial code was broken.
The code says: "Ministers are provided with facilities at government expense to enable them to carry out their official duties."
"These facilities should not generally be used for party or constituency activities," it adds.
Mr Ashworth told BBC Radio 4's Today programme: "What I am concerned about is that the Prime Minister seems to be conflating his ministerial role with his role as the member of parliament for Witney.
"I doubt he is inviting the leader of Leicester City Council, where I am an MP, or the leader of Manchester City Council into the No 10 policy unit to discuss ways to deal with the cuts.
"It feels like a breach and I hope the Cabinet Secretary will look into it."