In a letter to the director general, they said the BBC is “unfairly representing” Leave voters by focusing on those who regret their decision.
The MPs warned the future of the BBC “will be in doubt” if it is not seen as a impartial broker.
The BBC said it was its job to “scrutinise and analyse” Brexit issues.
The letter was organised by Conservative MP Julian Knight, a former BBC journalist who backed Remain but says that has not stopped him disagreeing with the stance of the coverage.
It was signed by 60 other Tories including Iain Duncan Smith and Theresa Villiers.
Two Conservative peers, three Labour MPs, eight DUP MPs, two DUP peers and UKIP’s only MP, Douglas Carswell, also added their names.
‘Future in doubt’
They said the BBC’s inability to break out of “pre-referendum pessimism” and to accept new facts was skewing its coverage of Brexit.
“If politicians and the public don’t view it as an impartial broker, then the future of the BBC will be in doubt,” the letter stated.
It said many Leave-voting constituencies have felt their views have been unfairly represented by the BBC.
“This phenomenon is weakening the BBC’s bond with the 52% who voted Leave and all who wish to make a success of the decision made,” it added.
MPs also claimed the BBC had “skewed” good economic news since the referendum and “licence fee-payers have the right to expect better”.
The letter, which was also copied to the incoming chair of the BBC Board Sir David Clementi, did not include any specific examples.
It is best understood as a warning from the BBC’s detractors that they expect a reasonable hearing in the Brexit negotiations in Europe, says the BBC’s media editor Amol Rajan.
‘Job to scrutinise’
The MPs said BBC bias can have a substantial effect on the national debate and its coverage also shapes international perception of the UK.
“We fear that, by misrepresenting our country either as xenophobic or regretful of the Leave vote, the BBC will undermine our efforts to carve out a new, global role for this country,” they added.
The MPs urged the BBC to take steps to “correct these flaws” in its Brexit coverage.
A BBC spokesman said: “While we are always live to our critics and understand that passions are running high on all sides of the debate, it is the job of the BBC to scrutinise and analyse the issues on behalf of the public and to hold politicians to account across the political spectrum.
“That is what the BBC has been doing. It is what the BBC will continue to do. It is precisely because of this, that the public trusts the BBC.”
That final statement has to be a joke!