Bank of England governor Mark Carney has sought to calm financial market fears about the impact of the UK’s Brexit vote by insisting that Threadneedle Street will take any measures needed to secure economic and financial stability.

In a statement choreographed to follow David Cameron’s announcement that he intended to step down as prime minister, Carney said contingency plans drawn up by the Bank and the Treasury would now swing into action.

The Bank governor said UK banks were in better shape than they were before the 2008 financial crisis. But he added that he was prepared to inject an additional £250bn to ensure that financial institutions did not run short of cash during what he admitted would be a period of uncertainty.

The Bank has also set up arrangements with other central banks around the world to provide foreign currency to the UK markets should that be required.

Stressing that some market and economic volatility was to be expected in the aftermath of the Brexit vote, Carney added: “But we are well prepared for this. The Treasury and the Bank of England have engaged in extensive contingency planning and the chancellor and I have been in close contact, including through the night and this morning.”

Some City analysts expect the Bank to boost the economy by cutting interest rates or re-starting the money creation programme known as quantitative easing, but Carney made it clear that Threadneedle Street would not be rushed into decisions by the shock nature of the referendum result.

“In the coming weeks, the Bank will assess economic conditions and will consider any additional policy responses”, he said in a statement.

The Bank said in its quarterly inflation report last month that Brexit poised the most significant threat to the UK’s financial stability.

Carney said that in order to mitigate those risks the Bank had ensured the financial system was “well-capitalised, liquid and strong”, adding that it would ensure that market remained orderly.

The economy would adjust to new trading arrangements that would be put in place over time, the governor said, noting that the Bank’s job was to ensure its responsibilities of keeping inflation under control and the financial system stable.

“These are unchanged. We have taken all the necessary steps to prepare for today’s events. In the future we will not hesitate to take any additional measures required to meet our responsibilities as the United Kingdom moves forward.”