The Tories are at the centre of a fallout today after their press office page rebranded itself as "factcheckUK" during last night's leadership debate.
Labour's David Lammy was among those to criticise this, calling the action "grimly dystopian" and likening it to the future written about by George Orwell in 1984.
Responding to a video of Mr Cleverly defending the tactic, Mr Lammy wrote on Twitter: "Grimly dystopian. James Cleverly lies about using the Conservative Party Press account to lie to the country by pretending it is fact-checking service calling out lies, when in fact it is spreading more lies. This is what George Orwell wrote about in 1984."
Following this, Mr Cleverly shared a screengrab of a Twitter account named The Insider, a Labour-run account.
Its description reads: "Trust the facts, not the waffle. @UKLabour account giving you facts, information and comment you can trust."
Along this, Mr Cleverly wrote: "So David, are you also going to call out this 'fact-check' site? Is this 'grimly dystopian'?
"It is a Labour Party account and website. Your hypocrisy is breathtaking."As the spat unfolded, Mr Lammy responded to say the Labour page does not claim to be a fact checking page.
He wrote: "The page you have found doesn't say 'fact-check'.
"You rebranded the Tory Party press page as 'FactCheckUK' in order to con the public. Just like you doctored a video of Keir Starmer.
"For treating the British people like idiots, you should be ashamed."
Mr Lammy referred to an edited version of an interview with Keir Starmer which CCHQ cut short, which made it appear Sir Keir did not have an answer to a question put to him on Brexit.
Amid the furore, Mr Cleverly previously told the BBC: "I'm absolutely comfortable with them calling out when the Labour Party put what they know to be complete fabrications in the public domain."
As the Tories moved to defend their actions, foreign secretary Dominic Raab said "no one gives a toss" about the "social media cut and thrust" when quizzed over the Tory press office's Twitter rebranding as a fact checking organisation during last night's debate.
The Conservative Campaign Headquarters press office account, followed by nearly 76,000 users, changed its name from its usual CCHQPress, while switching its display image to a white tick against a purple background during last night's debate.
Twitter has blasted the moved and said any further similar shenanigans could result in action being taken by the platform.