"Uncertainty around demand for new forms of digital money is why the Bank is considering the need for limits to manage the transition period as they emerge."
Officials are looking at setting up a central bank digital currency (CBDC) whereby individuals could gain access to sterling in the form of central bank reserves, a type of currency only currently available to banks.
This could be used directly by individuals as a digital form of the banknotes issued by the Bank of England, instead of the commercial bank money that households typically hold in their current accounts and use when making bank transfers or using their debit cards.
But privately created "stablecoins" are another option that could fulfil a similar purpose in letting people make digital transactions.
"We live in an increasingly digitalised world where the way we make payments and use money is changing rapidly," said Andrew Bailey, the Bank's Governor.
"The prospect of stablecoins as a means of payment and the emerging propositions of CBDC have generated a host of issues that central banks, governments, and society as a whole, need to carefully consider and address. It is essential that we ask the difficult and pertinent questions when it comes to the future of these new forms of digital money."
The Bank is watching closely for any risk of this threatening financial stability or customers' ability to access credit and the payments system – for instance if a shift appears likely to happen very rapidly. However it believes banks will settle on new sources of funding over time.
It is not thought to have an interest in taking action to preserve the banking system in its current form purely for the sake of the incumbent financiers, if customers find new digital currencies more convenient, safer or cheaper than the current system.
Officials at the Bank modelled a situation in which households and businesses move a large chunk of uninsured deposits into a new stablecoin, on the basis that this could be perceived to be a safer option, amounting to roughly one-fifth of bank deposits.
"As a result of this potential outflow, commercial banks would have to adapt their balance sheets in response to maintain their current liquidity ratios. An increase in banks' funding costs is assumed to increase rates on new bank lending, while some borrowers may find it cheaper to seek credit opportunities in the non-bank financial sector," the Bank of England said.
Sir Jon Cunliffe, one of Mr Bailey's deputies, said there could be a range of benefits from a digital currency, including reducing costs compared with the fees charged to use credit cards, but also potentially "programming" the digital money to control how it is used.
"You could think of smart contracts in which the money would be programmed to be released only if something happened," he told Sky News.
"You could think of giving your children pocket money, but programming the money so that it couldn't be used for sweets. There is a whole range of things that money could do, programmable money, which we cannot do with the current technology."