Both companies secured contracts with the Nigerian National Petroleum Corporation (NNPC) or its subsidiaries, according to the prosecution.
The former minister is also said to have received £100,000 ($230,000) in cash, chauffeur-driven cars, a private jet flight to Nigeria and refurbishment work and staff costs at several London properties.
Other counts allege she received bribes, including school fees for her son, products from high-end shops such as the Harrods department store and Louis Vuitton, and further private jet flights.
Alison-Madueke, who was president of the Organisation of Petroleum Exporting Countries (Opec) for one year between 2014 and 2015, has been involved in numerous legal cases around the world, including in the United States.
In Nigeria, several properties belonging to her and valued at several million dollars were seized by courts in 2017.
A spokesperson for Nigeria’s Economic and Financial Crime Commission (EFCC) confirmed that the agency had “some subsisting cases against her”, without giving additional details.
Alison-Madueke has been on bail since she was first arrested in London in October 2015. She has denied the charges against her.
In 2023, she was formally charged with accepting bribes.
“We suspect Diezani Alison-Madueke abused her power in Nigeria and accepted financial rewards for awarding multi-million-pound contracts,” the UK National Crime Agency (NCA), which targets international and serious and organised crime, said at the time.
Two others, Doye Agama - her brother - and Olatimbo Ayinde, are also being prosecuted on bribery charges linked to the case.
All three defendants had a British address at the time of the alleged offences, according to the prosecution.
Judge Justine Thornton said she hoped the trial would end by April 24.
-Agence France-Presse