Rose had been identified as the source of information given to an inaccurate BBC report after GB News presenter Nigel Farage had his Coutts bank account closed.
The Dame admitted to a "serious error of judgement" but her resignation hasn't stopped calls for the rest of the board at NatWest - the bank who owns Coutts - to step down.
Farage himself has called for the board to resign and former MEP Ben Habib agreed when he joined Eamonn Holmes and Ellie Costello on Wednesday's Breakfast with Eamonn and Isabel.
Discussing Rose's resignation, Habib warned: "If people think this is the end of it, I'm afraid they are sadly mistaken.
"As Nigel said, this is only just beginning," he added while Holmes had his own scathing criticism of Rose's exit statement.
The GB News host branded the statement as a "load of sorry but not really sorry" before he took aim at the banking world as a whole following the debacle.
Nigel Farage discussed Rose's resignation on Wednesday's GB News
GB NEWS
"Let's stop this in their tracks that institutions, that corporations can be our moral guardians of certain things," he raged.
"It's none of their business, nothing to do with them.
"Shut up, take our money, let us bank with you or not as the case may be."
Holmes turned to co-host Costello as he mused: "It got me looking at all the adverts which are running on television now.
"I know these banks were not necessarily involved in this but all that, 'Here by your side,' and, 'Let us make your money work for you,'... all this sort of nonsense.
"All this cuddly, friendly - they would knife you in the back, or knife you in the front actually as soon as they'd look at you.
"So what's it got to do with you? Shut up, take the money, that's all you've got to do!"
In her resignation statement - which came less than 24 hours after NatWest said they'd stand by her - Rose thanked her colleagues for their support.
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Eamonn Holmes and Ellie Costello also heard from Ben Habib
GB NEWS
She went on to add: "I remain immensely proud of the progress the bank has made in supporting people, families and business across the UK, and building the foundations for sustainable growth."
Farage claims he's been rejected by 10 banks in total as the scandal continues.
The incident began last week when Farage produced a 40-page dossier which revealed that his Coutts account was shut predominantly as a result of his political views.
According to the finding, these were said to be at odds with the bank’s values.
However, this catalogue of evidence contradicted the BBC which ran a story claiming the account closure was as a result of to Farage failing to meet a £1million borrowing requirement.
The BBC ended up apologising to Farage, as did business editor Simon Jack, as they claimed the information was from a "trusted source".