Britain's bankers are pushing for transitional arrangements to soften the impact of Brexit.
Banks are currently adopting a “wait and see” approach on whether to remain in the UK, according to the chief executive of the British Bankers' Association, but Browne said that transition measures could soften uncertainty and the risks of a “cliff edge” of market disruption.
Anthony Browne told a House of Lords EU committee that while banks were awaiting more details, the failure to provide framework for change would force them to decide on relocation, because the moves would take several years to implement.
"What we would like ... is to have as full bilateral access to the European market as close as possible to what we have at the moment," Browne said.
Browne's comments come after Lloyd's of London chairman John Nelson warned earlier this week that insurers could choose to transact business in Europe without the UK is unable to secure passporting rights for firms.
Meanwhile, chancellor Philip Hammond this morning met with a senior City lobbying group at the Treasury.
After meeting with the European Financial Services Chairmen's Advisory Committee – led by Santander's Shriti Vadera – earlier today Hammond said he was determined to listen to the financial services sector on issues like the Single Market.
“We want the best deal for trade in UK goods and services, including our world leading financial services industry,” Hammond said.
“It is important Britain maintains its status as a great place for financial services and that is why the government stands ready to help the sector maximise the opportunities that leaving the EU presents."