The penalty was given to the firm for failing to keep proper records of payments to an adviser in Tanzania and followed a controversial plea bargain at the end of six years of investigations by the SFO.
It was announced in February that a deal had been struck between prosecutors and the company, provoking anger by those who wanted it held to account in court over bribery allegations.
Under the deal, BAE was to pay $400 million to the US Department of Justice and plead guilty to one charge of conspiring to make false statements to the US government relating to its operations and business dealings in the Czech Republic, Hungary and Saudi Arabia.
It would also pay 30m in the UK for failing to keep "reasonably accurate" accounting records over activities in Tanzania - the SFO's largest settlement with a UK company.
Southwark Crown Court yesterday heard that payments totalling about $12.4m (7.7m) were made to two companies controlled by Tanzania-based businessman Shailesh Vithlani between January 2000 and December 2005.
The court heard BAE believed Mr Vithlani was probably given the money for helping it to win a $40m (25.8m) contract to provide a radar system for Dar-es-Salaam international airport in Tanzania.
BAE pleaded guilty to one count of breaching its duty to keep accounting records, contrary to section 221 of the Companies Act 1985.
Judge Mr Justice Bean criticised the settlement agreement, saying it was "loosely and perhaps hastily drafted". He highlighted paragraph eight, whereby the SFO agreed on "no further investigation or prosecutions of any member of the BAE Systems Group for any conduct preceding 5 February 2010".
The judge said: "It is relatively common for a prosecuting authority to agree not to prosecute a defendant in respect of specified crimes which are admitted and listed in the agreement. This is done, for example, where the defendant is an informer who will give important evidence against co-defendants.
"But I am surprised to find a prosecutor granting a blanket indemnity for all offences committed in the past, whether disclosed or otherwise.
"The US Department of Justice did not do so in this case. It agreed not to prosecute further for past offences which had been disclosed to it."
The judge said he had no power to vary or set aside the agreement.
"Indeed, an attempt by the pressure group Campaign Against the Arms Trade to challenge it by way of judicial review, arguing that the SFO should have brought corruption charges, was rejected by Mr Justice Collins on 24 March, 2010.
"The judge held that it was not arguable that the decision to limit the charge to one under section 221 was unlawful."
He added: "I also cannot sentence for an offence which the prosecution has chosen not to charge. There is no charge of conspiracy to corrupt, nor of false accounting contrary to section 17 of the Theft Act 1968."
Mr Justice Bean pointed out that on the basis of the documents shown to him "it seems naive in the extreme to think that Mr Vithlani was simply a well-paid lobbyist".
He accepted that there was no evidence BAE was party to an agreement to corrupt.