The U.K.'s main opposition party says a move would benefit the wider economy.
The suggestion came as part of a report, commissioned by the Labour Party, designed to probe at the effectiveness of the relationship between the U.K.'s financial system and the rest of the economy.
Consultants have concluded that the central bank's base on Threadneedle Street in the City of London, where it has been located since 1734, is "unsatisfactory and leads to the regions being underweighted in policy decisions." From 1694 to 1734, the BOE was based nearby at Cheapside.
The report, compiled by GFC Economics, said that Birmingham would be a better hub for some of the BOE's functions and that a new location should also house a National Investment Bank as well as a Strategic Investment Board.
"All three, side-by-side, would constitute a new 'economic policy' hub, possibly close to the main train station," read the report, released Sunday.
The study also called for the BOE to create new regional branches in Glasgow, Cardiff and Belfast.
The Labour Party is currently neck-and-neck with the ruling Conservative Party in opinion polls. The next U.K. general election is not scheduled to be held until 2022.
The report's authors also claimed that the U.K.'s financial system is failing the country's technology firms.
"As a central bank sitting at the heart of the U.K. financial system, the Bank of England needs to be playing an active, leading role, ensuring banks are helping U.K. companies to innovate," said Graham Turner, chief economist at GFC Economics. "Flow of funds analysis shows that banks are diverting resources away from industries vital to the future of this country."