The Bank of England has said a transition period after the Britain leaves the European Union would give banks more time to make orderly changes as Brexit poses risks to financial stability.
With UK due to leave the bloc in March 2019, the BoE's Prudential Regulation Authority (PRA) said it faces heavy demands from Brexit fallout on banks and insurers.
BoE Deputy Governor and PRA Chief Executive Sam Woods said "some form of implementation period is desirable" between Britain leaving the bloc and start of new trading terms to "give UK and EU firms" more time to make necessary changes.
But he stopped short of saying what sort of transition he wanted in a reply to Nicky Morgan, new chair of parliament's Treasury Select Committee, who asked him this month for his views on the design of such a period.
The UK government has not presented the EU with any firm request for a transition period as it still seeks internal consensus.
UK-based firms are not waiting for clarity and are announcing new hubs in the EU27 to be sure of serving customers there after March 2019 - and avoid the destabilising ruptures in financial links the BoE fears.
Mr Woods had asked banks to spell out how they would cope in particular with a "hard" Brexit where Britain crashes out of the EU with no transition or trading deal.
In a letter to Morgan made public on Wednesday, he said 401 responses were received, which revealed "significant issues for many firms" and the BoE will reach a view on the plans in the autumn.
The submissions provided "further evidence" of risks the BoE had already identified, specifically relating to the continued servicing and performance of existing contracts and restriction on data transfers.
There could be a sharp rise in the number of insurance policies shifted from one country to another, a switch that involves the courts, he said.
The Association of British Insurers said insurers fear they will be left with a stark choice between breaking their promise on millions of policies with customers, or breaking the law regarding payouts on cross-border contracts still in force after Brexit.
"Agreeing terms to allow insurers to service contracts after March 2019 needs to be part of the exit negotiations between the UK and EU," said Huw Evans, director general of the ABI.
The BoE's Woods said that re-structuring by financial firms to mitigate risks to their business will in general increase complexity, while dislocation and fragmentation of markets could bump up costs and cut activity.
The BoE will need to ensure that supervising firms with links between the EU and a Britain outside the bloc, is still doable, he added.
The PRA faces having to authorise and supervise a significant number of additional firms, which could place a material extra burden on resources, Mr Woods said.
London is home to branches of banks from continental Europe and they face having to become subsidiaries, meaning they would be directly supervised by the PRA.
Mr Woods said the issues set out in his response to Morgan "pose a material risk" to the PRA's objectives as a supervisor, and that this work is a top priority.
"It is incumbent on us to manage this burden but we may have to make some difficult prioritisation decisions in order to accommodate it," he said.