A family source confirmed to PEOPLE that the couple have been separated since May, amid news that McGregor was spotted kissing his co-star Mary Elizabeth Winstead.
On Sunday, photos of the Trainspotting and Star Wars actor, 46, kissing his Fargo co-star, 32, at a West London cafe were published by The Sun.
In February, Winstead shared a photo with McGregor on her Instagram with the caption, 'Pretty lovely Canadian Sunday. Good night!'
McGregor met Mavrakis on the set of the British TV crime series Kavanagh QC and they were married in 1995.
The couple have four daughters together: Clara, 21, Jamyan, 16, Esther, 15 and Anouk, 6.