According to Woods, this would make such firms more complex and hard to supervise because of strong UK-EU interconnections.
Woods also said the PRA faces a "material risk" to its mandate to supervise banks, and that Brexit places "an extra burden" on the regulator's resources.
In a final point, Woods told Morgan the authorisation and ongoing supervision of a significant number of additional firms was likely to overburden the PRA's resources.
Woods added that risks to financial stability will deepen due to Brexit, as he gave his backing to securing a transitional exit deal.
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 European Union and a Britain outside the bloc, is still doable, he added.
The Bank may end up regulating more firms if there is no deal on passporting, the system through which some insurance companies and banks based in the EU, Iceland, Liechtenstein and Norway are able to operate in the United Kingdom without Bank of England authorisation.
He also warned that the regulator could suffer a significant "material extra burden" by having to regulate more firms when Brexit is undertaken and noted that this and several other concerns posed "a material risk to our objectives, and this work is therefore a top priority".
Trump's 'fire and fury' parallels North Korean rhetoric
To build a nuclear weapon, Brumfiel says, you start with a lot of conventional explosives that trigger the nuclear chain reaction. North Korea began producing fissile material for bombs in the 1990s and conducted its first nuclear test explosion in 2006.
Atlanta gym bans police officers, military from joining
According to Chambers, users of the gym are usually minorities who would not feel comfortable with police officers inside. But, he added that his gym has never required the help of officers, and said that they will never need it, either.
Busted! BBC Employee Caught Watching Adult Movie on Air
Presenter Sophie Raworth had absolutely no idea a saucy scene was being shown on a screen behind her on Monday evening (August 7). It is totally unprofessional. " The employee is on borrowed time when bosses catch up with him ".
Chicago sues White House for sanctuary cities plan
Sessions accused the city of open hostility to enforcing immigration laws and said they are protecting, quote "criminal aliens". Among the other bigger USA cities with such policies are NY and Philadelphia.
Chris Sale is great, but he's not Pedro Martinez
He plowed through his rehab assignment on August 5, striking out six over 3.0 innings during High-A Charlotte's loss. Red Sox infielder Dustin Pedroia was activated off the 10-day DL and batted in the two hole as a designated hitter.
Trump's support among his base is collapsing
The majority of voters said Trump was not honest and 65 percent said they believe his campaign colluded with Moscow in some form. He leads 51 percent to 42 percent among registered Republicans and 54 percent to 37 percent among independents.