Tony Blair, the British prime minister, said he took full responsibility for stopping the investigation and that the UK's relationship with Saudi Arabia was crucial for counter-terrorism and Middle East peace.
Campaign groups The Corner House and Campaign Against Arms Trade have said that the government's action was in breach of the Organisation for Economic Co-operation and Development's Anti-Bribery Convention.
The convention came into effect in 1999 and requires signatories to classify as a crime the payment of bribes to foreign public officials in international business transactions.
The campaign groups said: "The decision was based on considerations of potential damage to relations with Saudi Arabia. This is expressly forbidden under the OECD's Anti-Bribery Convention.
"The advice given by the prime minister amounted to a direction to discontinue the investigation, which is an unlawful interference with the independence of prosecutors under domestic and international law".
Lawyers for The Corner House and Campaign Against Arms Trade wrote to Blair, Lord Goldsmith, the attorney-general for England and Wales, and Robert Wardle, director of the Serious Fraud Office, stating that the groups would formally seek a judicial review unless the government reversed its decision by January 2.
Separately, the Liberal Democrats said they were finalising a demand for a vote to force the government to publish a 1992 national audit office report on the Al Yamamah contract.
"It is unprecedented for the national audit office to prepare a report for a committee of this house and for it not to be published. This house, if it has any integrity, will insist on the publication of that report," said David Heath, the Liberal Democrats parliamentary spokesman.
"There is a great danger that we are seen as a country to prosecute in the case of weak countries without oil or strategic interests and not to be prepared to continue a case in the incidence of a country which we have a strategic interest in protecting," he said in the UK parliament's last session of the year.
The original Al Yamamah deal was struck in the mid-1980s between the British and Saudi Arabia governments, when BAE was appointed the prime contractor.
The Liberal Democrats said BAE and its predecessor, British Aerospace, earned $84bn in 20 years from the contracts.