The Cheshire Record Office Catalog has this note for Marton "Marton was one of a number of Cheshire chapelries which lost the right to solemnize marriages between 1754 and the mid-19th century. Marriage entries for those years will be found in the registers of the mother parish of Prestbury.". This was a result of Hardwicke's marriage act.
The earliest they would have restarted would be at the start of civil registration. However, a few searches on Cheshire BMD, suggest that marriages restarted around 1889. I could not find these registers in the CRO catalog.
Regards,
Deryck