Some UK-based financial services firms have already decided to relocate at least part of their operations to Ireland, the Minister of State for Financial Services has said.
Others are expected to follow in the first half of this year, Eoghan Murphy added.
Speaking at an event hosted by the London Irish Business Society and PR firm Powerscourt, Mr Murphy said the UK decision to trigger divorce negotiations from the EU at the end of March had been a catalyst for these moves.
"With the time horizon we now have around Article 50, some decisions have already been made for relocation," Murphy said, declining to name the companies, or give a number.
"We are expecting for some parts of the industry for decisions to be made in Q1 and Q2," he added at the business event in London.
Barclays is preparing to make Dublin its EU headquarters when Britain leaves the European Union, a source familiar with the matter told Reuters last week.
Central Bank Governor Philip Lane said he expected economic ties between Britain and Ireland would remain close after Brexit.
He added that no other European capital would become a "new London" - though a collection of centres specialising in different financial services was possible.
Philip Lane, who is also a member of the European Central Bank's Governing Council, said Europe's future financial centres may be more fragmented geographically, even if they were integrated as part of a single market.
Cities around Europe are already vying for the potential new business, including financial centres in Germany, France, the Netherlands, Luxembourg and Ireland.
"There is not going to be any new London in the EU 27. History happened in a certain way. You can't just lift institutions and drop then somewhere else," Professor Lane said at the London Irish business society event.
"You may well have this fragmented but integrated financial system so location X has a cluster of derivatives trading, location Z has a cluster of insurance etc," he explained.
The UK government and Bank of England have highlighted the rest of Europe's reliance on London for financial services.
They have warned that a tough approach to the Brexit talks from the European Union risked jobs moving to the US or Asia, rather than elsewhere in Europe.
Mr Murphy said that some financial services firms wanted to keep quiet their plans to move some operations but leave others to avoid antagonising British stakeholders.
"Some companies are going to be very mindful of the presence they have. They are not going to be coming out and saying 'Brexit is a disaster, we are moving people to Ireland'."
"So while the decisions have been made and movements will happen they won't necessarily be announced as Brexit decisions, so we can't put numbers on them," he said.
He added that after the two years of formal Brexit talks conclude, he expected there would need to be at least a five-year transitional agreement between the EU and Britain before a complete divorce could take effect.