The jury at Snaresbrook crown court heard that security supervisor at the bank, Kevin O'Donoghue, had repeatedly admitted two Belgian hackers - Jan Van Osselaer and Gilles Poelvoorde - to the bank's offices in the City, the Times reports.
Once inside, they are alleged to have installed spyware that recorded employees' passwords and other security information.
The men are then said to have attempted to transfer money to accounts set up by accomplices in Spain, Dubai, Hong Kong and Singapore.
However, the prosecution said they failed because they were unfamiliar with the Swift money transfer system and repeatedly entered incorrect data.
Two British businessmen, Bernard Davies and Hugh Rodley, are accused of setting up the overseas accounts to launder the stolen funds.
Mr O'Donoghue, Mr Osslaer and Mr Poelvoorde admitted their roles in the conspiracy.
Mr Rodley and two other men, David Nash and Inger Malmros, deny the charges. Mr Davies passed away before the trial.
The case continues.