Minutes of last month's meeting by the Financial Policy Committee (FPC) revealed concerns that the threat of cyber attacks "had many dimensions and was growing".
The FPC, which is charged with safeguarding financial stability, cautioned there were a number of "potential vulnerabilities" in the banking system and said it wants banks and other institutions - including the Bank of England - to draw up plans for protection as a priority.
The UK's banking sector is particularly at risk due to old and complex IT systems, as well as a high degree of interconnectedness and its reliance on centralised infrastructure, such as payment systems and clearing houses.
Treasury officials are already working on plans to assess, test and improve the system's resilience to cyber attacks.
But the FPC, which is c haired by Bank governor Mark Carney, said there now needs to be a "concrete plan" in place by the end of the first quarter of 2014, with a progress report before the end of this year.
Alongside the cyber concerns, the FPC has already confirmed it is keeping a close watch over the UK's housing market, last week issuing a statement from the meeting on September 18 confirming it was " vigilant'' and ready to act to prevent another bubble that could threaten financial stability.
The Bank also separately today published plans on how to stress test banks each year, proposing to initially limit the exercise to the eight largest players - HSBC, Barclays, Royal Bank of Scotland, Lloyds Banking Group, Standard Chartered, Santander, Nationwide Building Society and Co-operative Bank.
It has launched a consultation on the stress tests, with a deadline for feedback set for January 10 next year.