Damian Collins, the high-profile chair of the Digital, Culture, Media and Sport (DCMS) committee, ramped up his criticism of Mr Cummings, saying there needed to be "real-world sanctions" for those who defy MPs.
The decision to appoint Mr Cummings to a senior post at No10 took Westminster by surprise, coming only months after he was found in contempt of parliament for repeatedly refusing to appear before the DCMS committee's fake news inquiry.
The committee wanted to grill Mr Cummings over Vote Leave's use of data on social media during the Brexit referendum, where he is seen to have played a crucial role.
Asked whether Mr Cummings should have been appointed, Mr Collins told the Edinburgh television festival: “I think we have a very inadequate situation where there’s not enough real-world sanctions for those found in contempt of the house."
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"There should be some sanction for those found in contempt of parliament, including whether they should be considered fit to hold public office," he said, according to The Guardian.
The intervention comes in spite of Mr Collins' support for Mr Johnson in the Tory leadership contest, when he argued that the new prime minister was the only person to restore "trust and excitement" in politics.
However the Tory MP has frequently butted heads with Mr Cummings, who once leaked a confidential report by the committee, reportedly declaring “f*** the charlatans embargo” before posting the document on his personal blog.
The Brexiteer also refused the committee's summons and dismissed the charges of contempt - a symbolic admonishment that has rarely been used in modern times.
It comes after the Liberal Democrats wrote to Sir Mark Sedwill, the UK’s most senior mandarin, urging him to block the appointment.
Layla Moran, the party's culture spokesperson, said Mr Cummings' behaviour fell below Whitehall standards due to his admonishment for contempt and his involvement in Vote Leave’s “misleading” campaign about NHS funds.
Ms Moran told The Independent: “The appointment of Dominic Cummings should send shivers down the spines of UK citizens. This is a man who has peddled lies and flouted the truth for sheer, cynical political gain.
“The dark arts that he proffers should have no place in government, and no place in Downing Street."