The central bank study, which could have a major impact on the debate over Britain's future within the bloc, was due to remain confidential but details were accidentally emailed to an editor at The Guardian newspaper.
Cameron used an EU summit in Latvia to kick-start negotiations on changing Britain's terms of membership. He hopes to have a package of reforms to put to voters in an in-out referendum he has promised to hold by 2017.
"Today, information related to planned confidential bank work on the potential implications of a renegotiation and national referendum on the UK's membership of the European Union made its way into the public domain," the bank said.
"It should not come as a surprise that the bank is undertaking such work about a stated government policy.
"There are a range of economic and financial issues that arise in the context of the renegotiation and national referendum. It is one of the bank's responsibilities to assess those that relate to its objectives."
The bank said it was "not sensible" to discuss the project publicly but said it would disclose further details of the work "at the appropriate time".
On his first overseas trip since winning a general election two weeks ago, Cameron said he was "confident" of striking a deal on EU reform before the referendum, but warned that the process would involve "ups and downs".
The Conservative leader has said he would campaign to stay in the EU provided he can secure the changes, which include making it harder for EU migrants to claim state benefits in Britain.
Opinion polls currently indicate that Britons will vote in favour of staying part of the EU.