"The strategy we announced on March 1, 2016 was not conditional on the UK remaining in the EU. We are a transatlantic consumer, corporate and investment bank, anchored in the U.K. and the U.S.," Barclays chief executive, Jes Staley, said in a statement emailed to CNBC.
RBS said there would be no immediate impact on their services, but that time would be required for the bank to "work through the implications of the vote with regulators."
Bank of England Governor Mark Carney announced on Friday that the central bank would act to support U.K. financials and the broader economy as required.
"As a backstop, and to support the functioning of markets, the Bank of England stands ready to provide more than £250 billion ($343 billion) of additional funds through its normal facilities," he said in a public statement.
S&P Global Ratings said the "leave" vote would have no immediate impact on U.K. commercial banks' ratings.
"We see the effects of a leave vote on these banks as indirect, arising from potential adverse consequences for economic activity, new business volumes, asset prices, and demand for U.K.-related debt ... volatility may interrupt wholesale debt issuance and affect the values of financial assets in the near term," the ratings agency said in a report on Friday.