Mr Campbell is the editor of The New European, a pro-Remain newspaper launched after Britain voted to leave the European Union (EU) in 2019.
But the ex-spin doctor, a staunch critic of Brexit, spoke out after the BBC tweeted out the latest promo advert for its Daily Politics and Sunday Politics show.
Mr Campbell and Mr Farage debated Brexit on the show – but ahead of the slot, Mr Campbell aired his grievances on social media.
Tweeting a composition of Mr Farage smiling, and Mr Campbell frowning intently, the BBC cheekily tweeted: “Talking Brexit, so let’s get two neutral observers in.”
But just half an hour later, a seemingly infuriated Mr Campbell lashed back, tweeting at the BBC: “How come you have the nicotine-stained manfrog smiling and me looking like I’m at a funeral? Typical pro-Brexit BBC bias @RobBurl.”
Replying to Mr Campbell, one user, Mark Brandon, wrote: “The man who thinks he won and the man who knows everyone lost.”
On Friday morning, Tony Blair’s former Director of Communications told Alex Salmond on Russia Today that a “fatalistic” approach to Brexit would be a “Considerable cost” to the UK.
He claimed a “People’s Vote” was necessary, telling mr Salmond: “There is no doubt the public are confused and divided, just like Parliament is, I think the one thing that the Government is trying to play on and with some success is this fatalism let’s just get on with it.
“The important thing to be able to understand is that ‘lets just get on with it’ leads to the country doing the wrong thing and a considerable cost.”
Also appearing on Sky News on Friday lunchtime, Mr Farage, the former UKIP leader, shut down Remain-supporting Tory MP, Kenneth Clarke, with a list of EU policies he wanted scrapped.
Mr Clarke had suggested that Brexiteers could not cite any EU rules, prompting a furious response from MEP Mr Farage.
The pro-Brexit MEP said: “Common Fisheries Policy, Common Agricultural Policy, Working time directives. I could go on.”
He also dismissed attempts from Mr Clarke to undermine the position of Brexiteers, saying: “We want to be our own country, we want to govern our own country, we want to be independent people.
“We don’t want Mr Juncker governing us and a bunch go old losers in Brussels, we want to be free.”