The Bank admitted one of its suppliers had "misused" the feed to give hedge funds early access to information.
Danny Blanchflower, who previously served on the rate-setting Monetary Policy Committee, said Joanna Place should step down following the breach.
The pronouncements of central bank chiefs can sound like boring technical gobbledy-gook. But every word, every nuance, is carefully studied by financial markets for the slightest hint about the Bank's intentions and can cause big movements in the value of the pound and government bonds.
So getting wind of any potential future changes, even a few seconds ahead of the rest of the market, could be extremely valuable.
Computerised trading programs can execute thousands of transactions a second, so the four-to-eight second advantage enjoyed by those traders accessing the back-up audio feed is a vast amount of time in terms of market movements.
The Bank of England is usually very careful in managing the dissemination of sensitive information and the Bank was keen to stress that the information breach did not apply to the release of decisions on interest rates - just the press conferences afterwards. But those press conferences can - and do - move markets so this is still an embarrassing admission.
The Times said it had seen documents revealing how the service was sold on to traders. The supply cost between £2,500 and £5,000 each press conference for each client in addition to a subscription fee.
It is unclear whether the leaked audio feed was used by traditional traders at their desks to steal a march on rivals, or whether algorithm-driven software, that can conduct thousands of transactions a second, could be used to exploit those few seconds advantage.
Hypothetically a computer program could be designed to pick out key words from the Bank Governor's comments and trade on them. But central bankers are notoriously euphemistic.
"[Early access] would be more important to a traditional voice trader or hedge fund," says Malcolm Baker, co-Founder at FX FWD, a trading firm.
"Central bankers can speak in language that is hard to understand and there is a lot that's implied. It's like old Elizabethan language and can be misleading. A trader like me just wants to understand - is it hawkish? Or dovish?"
The Bank has not named the audio supplier, but market intelligence firm Statisma has posted a denial that it offers its customers information not available to the public.
Statisma, operating under the same management as a production firm called Encoded Media, advertises on Twitter a service where traders can hear central bank announcements first.
Press conferences from the European Central Bank, the US Federal Reserve and the Bank of Canada were also on offer to trading firms. Traders signed up to Statisma's service receive an email detailing the speeches with dial in numbers.
In a response to several calls made from the BBC and other media outlets, it posted on its website this statement: "We DO NOT carry embargoed information and we DO NOT release information without it first being made available to the public".
An ECB spokesman said the central bank moved to address possible issues with audio broadcasts in September, effectively delaying the feed.
"Since September this year the ECB offers a low latency audio feed for each monetary policy press conference to address exactly the issues that were in the news today.
"Therefore, it doesn't make any sense for anyone to use commercially offered solutions because the solution we offer is the fastest option available and it is free for everyone," the spokesman said.