Last month, Mr Storonsky hit out at the FCA over what he regarded as its slow procedures for processing applications, saying it was “slower compared to expectations”.
He added that it might be beneficial for the regulator to employ “more efficient people”, have “stricter timelines” and clearer performance indicators.
The watchdog has concerns around aspects of Revolut’s controls, culture and whether it has an appropriate number of employees to comply with “know your customer” checks and ongoing transaction monitoring, The Telegraph understands.
The FCA declined to comment. A spokesman for Revolut said: “We do not discuss ongoing license applications.”
While Ms Halligan was responsible for overseeing regulatory relationships and licenses at the most senior level of the business, Revolut also has specialist teams that focus on both areas, a source close to the company said.
Ms Halligan is leaving for a chief operating officer role at a company in her native Ireland.
The resignation is the latest in a series of senior departures at Revolut, which was valued at $33bn (£27.6bn) after its latest funding round last year.
In May, The Telegraph also revealed that Harry Gill, Revolut’s global head of regulatory compliance and a member of its executive leadership team, resigned following a restructuring of the company’s risk division.
Revolut’s head of operational risk and head of UK compliance have also left in recent months.
It comes as challenger banks face increasing regulatory pressure to tighten controls around financial crime and money laundering over fears they are cutting corners so customers can quickly set up accounts.
Revolut secured a challenger bank license from the European Central Bank in 2018, facilitated by the Bank of Lithuania, which allows it to accept deposits and offer consumer credit.
A Revolut spokesman said: “It’s critical that we continue to raise the bar when it comes to hiring and retaining the best talent. As a growing business, we have a role to play in removing barriers that women face and we are targeting 30pc senior leadership roles filled by women by 2025.
“Like other tech and financial services companies, we have a way to go to ensure that women are provided with fair and equitable opportunities here at Revolut.”
Ms Halligan was contacted for comment.