The Casino Royale star, 42, had been due to appear in the sci-fi film A Patriot before production was shut down in October 2019.
Ms Green is now suing production company White Lantern Films, claiming she is entitled to her $1 million (approximately £810,000) fee for the project, despite its cancellation.
Ms Green, who was both an actress and executive producer on the project, has claimed she is entitled to be paid her fee in the event that the production was cancelled under a so-called “pay or play” provision.
She is asking the court to rule that she is entitled to the money and that White Lantern should also pay her legal costs.
White Lantern Films is defending the case and bringing a counter claim against Ms Green, alleging she repeatedly made “unreasonable demands” and undermined the film’s production.
They have also claimed Ms Green repeatedly said she was ready and willing to take part in the film when she had no intention to do so.
The firm is claiming the one million dollar fee as well as seeking damages against Ms Green.
The trial in London is due to last eight days, with Ms Green due to give evidence on Monday.