Cllr Simon Henig, leader of Durham County Council, is also calling for a review of the Valuation Office Agency’s decision to write off the debt.
He said: “It seems that anyone working for the Prime Minister is exempt from the rules that apply to the rest of us.
“I have asked that all options to appeal this decision be considered.”
Mr Cummings ignored lockdown guidance to leave London and stay on the farm with his wife and son when they started experiencing coronavirus symptoms at the end of March.
They also famously made an ill-advised trip to Barnard Castle, around 30 miles away, on his wife’s Mary Wakefield’s birthday on April 12.
Mr Cummings said he was checking to see if his eyesight was good enough to drive.
It is believed he and his family had a council tax bill of between £30,000 and £50,000 written off.
Two properties, including Mr Cummings’ ‘lockdown cottage’ at the family farm near Durham, were built in breach of planning regulations.
They are now liable for council tax, the Valuation Office Agency (VOA) ruled last week.
But the VOA decided the charges at North Lodge Farm of around £3,000 a year would not be backdated to 2002 when the conversion was done.
Cllr Henig said he has asked his chief officers look into all possible options for an appeal of the national decision and believes the ruling should be justified in Parliament.
He added: “As a party that is committed to fairness, as soon as we were aware of a potential breach in regulations at North Lodge, council officers were instructed to investigate.
“There have been historical breaches of planning and building control regulation, which date back to the time of the former Durham City Council, but the current council was unable to take enforcement action due to the amount of time that had elapsed.
“People will want to know how, once again, the Government’s senior adviser is avoiding facing any consequences for breaching a set of regulations to which everyone else is expected to adhere.
“It is imperative the Valuation Office Agency be made accountable for this decision in Parliament so that public confidence in the council tax system be maintained.”
The VOA, which is part of HM Revenue and Customs, does not comment on individual cases, but said: “We treat all council taxpayers equally and in accordance with the law. Changes to show multiple self-contained units would not be backdated.
“If the property has remained in your ownership during the period when any changes were made there would not typically be backdated liabilities.”
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