The Channel 5 talk show, in which guests chat about current affairs discussed the topic of the state of the UK and Scotland's place in it on 25 June.
The discussion took place after Jeremy held up a newspaper with an article on Gordon Brown's comments on the Union as being in danger from “divisive nationalisms” threatening to “blow the United Kingdom apart”.
Guests included former Royal butler, Paul Burrell, who said that the Gordon Brown's words was "food" for Nicola Sturgeon but that he hoped the union would stay together and that Scotland wouldn't get devolution.
Mr Burrell continued: "I mean for goodness sakes...Scotland, by itself? How is it going to survive? What does it have? Oil...and a monster in a lake."
The remark provoked a backlash on social media with many nationalists condemning the comment.
The National reports that in the Ofcom complaint, the SNP say the broadcast was in breach of the broadcasting code, mentioning the lack of impartiality and Vine’s insistence in continuing the discussion despite a lack of a pro-independence voice.
Speaking to the newspaper on the party’s decision to lodge an official complaint, SNP media spokesperson, Hannah Bardell MP said: “This was one of the most inaccurate discussions about Scotland and independence ever broadcast on network television.
“That’s saying something given the level of nonsense Scottish audiences witnessed in the run-up to 2014.
“We’ll continue to work with journalists, editors and, where necessary as in this case, broadcasting regulators to make sure Scotland’s voice is heard – they are duty bound to ensure their programmes have due accuracy and due impartiality, not serve up guff like this.
“Ultimately the broadcasters are only harming themselves with embarrassing low-level output like this from Channel 5 – which will only make Scottish audiences switch over.”The broadcast watchdog argued Mr Burrell's comments were "personal views" and not the opinion of the channel.In a statement Ofcom said: "We regularly cover questions around Scottish independence on our daily current affairs programme, reflecting a broad range of opinions and voices.
“The comments expressed by the contributors in the programme reflect their personal viewpoints, not those of the channel.”