In the letter Sam Woods, chief executive of the PRA, said the bank expects all banks, insurers and investment firms with cross-border activities between the UK and the rest of the EU, including US banks with London subsidiaries, to undertake "appropriate contingency planning" for Brexit.
The PRA was created as a part of the Bank of England by the Financial Services Act in 2012 and is responsible for the prudential regulation and supervision of banks, building societies, credit unions, insurers and major investment firms.
While many firms are well-advanced in planning, the PRA believes planning is "uneven", and "plans may not be being sufficiently tested against the most adverse potential outcomes", Woods said.
Financial firms should therefore send the PRA written confirmation that management has considered contingency plans by July 2017, along with a short summary of these plans and assurance that they address a wide range of scenarios, he said.
The PRA will use the responses in its own planning and will share the information with the Financial Conduct Authority, Woods said.
Banking expert Tony Anderson of Pinsent Masons, the law firm behind Out-Law.com said: "This is a sensible way for the PRA to gauge the state of planning across the financial sector with a view to achieving a level of consistency across its various markets and participants. This approach is crucial given the interconnectedness of participants and the risk of systemic failures where there are gaps in contingency planning."
On the same day the letter was sent, Bank of England governor Mark Carney told an audience in Canary Wharf that financial reform over the past decade has created a "safer, simpler and fairer" financial system, the benefits of which are beginning to be realised but that could be damaged by Brexit.
"The global financial system is moving from fragility to resilience. The too-big-to-fail public subsidy enjoyed by private systemic banks has fallen by 90% in the UK. Credit is now growing in all major economies. Sources of finance are increasingly diversified between banks and markets, helping to keep the cost of finance low. And the system is demonstrating an ability to dampen shocks rather than amplify them," Carney said.
We are, however, now at a "fork in the road", with two potential paths, he said: one building on the foundations that have been put in place and creating a system of "enhanced equivalence and mutual deference", or "another path … where trust and cooperation diminish, fragmentation hardens, capital flows are disrupted, and trade and innovation are curtailed".
"The outcome of the Brexit negotiations could prove highly influential in determining which path the global financial system takes," Carney said.