The Scottish MPs claimed the corporation was bias during the 2014 Scottish independence referendum. A letter to the broadcaster was signed by Scotland’s former justice secretary Kenny MacAskill, Angus MacNeil, Douglas Chapman and Neale Hanvey.
In their letter, they demanded the abolition of the TV licence in Scotland, devolution of broadcasting, powers for Holyrood to set broadcasting tax, a Scottish government-funded BBC Scotland and consultation to improve engagement.
Mr MacAskill said: “If this situation continues and the crisis worsens then it may very well be there is no alternative.
“I for one will not pay a licence fee for Tory propaganda.”
However, the letter – which was published in The National newspaper – provoked a split within the party.
Glasgow South MP Stewart McDonald likened the campaign to President Donald Trump’s style to “defend public service broadcasting”.
He tweeted: “Trump is running a campaign to defund public service broadcasting in the US.
“We’ve got nothing to gain by running a parallel campaign against the BBC – no matter how frustrating you may find it.”
A BBC spokesperson responding to the letter saying they will respond in “due course”.
READ MORE: BBC ordered to scrap TV licence fee – poll
The licence fee is the annual cost viewers must pay in the UK and funds the TV, radio and online services of the BBC alone.
Those caught watching television without a licence can be fined up to £1,000 in addition to court costs.
Last month, BBC staff were warned by the new Director General Tim Davie the future of the corporation is in doubt.
In a bid to make a clear cut from the past, Mr Davie demanded the corporation renew its image of impartiality and warned staff if they are unable to avoid being bias, they should not be working at the BBC.
He warned staff he will be taking action in coming weeks and revealed there will be new guidance on how to best deliver impartiality.
Mr Davie also announced he wants a “radical shift” in the focus of the BBC as it attempts to reconnect with viewers who feel alienated by the corporation.
He also added there is no room for complacency in the future and said the BBC’s future was at stake.
The BBC has faced scrutiny over equal pay and diversity with an Ofcom report last year revealing it is seen as too white, middle class and London-centric.
Mr Davie previously seemed open to the idea of a subscription service, like Netflix, as calls erupt to defund the BBC.