Supporters, including families of the six men, handed in the petition urging Prime Minister David Cameron to intervene.
They have also launched a campaign to raise money for a "fighting fund" to help their loved ones in prison.
Billy Irving, from Connel, Scotland; Nick Dunn, from Ashington, Northumberland; Ray Tindall from Chester; Paul Towers, from Yorkshire; John Armstrong from Wigton, Cumbria, and Nicholas Simpson, from Catterick, North Yorkshire, were arrested on October 12 and have been in prison in India since October 24.
The men were working for US private maritime company AdvanFort providing anti-piracy protection when their ship was detained.
According to the men, Indian authorities claim that the vessel had entered Indian waters illegally with weapons on board, despite AdvanFort apparently insisting that the ship had the correct papers.
A petition, set up on online platform Change.org, calls on the Government to step in and help the men.