An elderly English woman named Amy Wilkinson, almost at her deathbed in London due to a blood clot caused by a past head injury, wants to come down to Madras in search of a man named Ilam Parithi, whom she last saw on 15 August 1947. She wishes to return a thali (traditional wedding threads) belonging to his mother, which he gave her as a sign that she belongs to India and nobody can separate them. However, after a turn of events, she had married another man from her hometown and thus felt that the thali was no longer her property.

Amy arrives in Madras with her granddaughter Catherine, equipped only with a picture of Parithi that was taken 60 years ago. Amy interrogates various people about Parithi's whereabouts. In the process, she recalls the events when she had first visited Chennai, and the chain of events that took place.

A young Amy, the daughter of the Madras Presidency Governor, George Wilkinson, visits Chennai (then called Madras, with the Chennai District being called Madrasapattinam) along with her translator Nambi and encounters Parithi, whom she calls a "brave man". Parithi, a member of the dhobi (washermen) clan, is also an experienced wrestler who trains under Ayyakanu. He openly opposes the British officials who attempt to build a golf course in the dhobi clan's dwelling place. He challenges a cruel racist officer named Robert Ellis, who is also Amy's suitor, to a wrestling match to decide the fate of his clan's home. Parithi is successful, and Ellis vows revenge.

In between this, the scene shifts to the present day where the aged Amy, who is going around Chennai looking for Parithi, starts remembering the olden days. She and Catherine go in a taxi driven by Veerasekhara Murali and his assistant. They track down an old woman named Selvi (as Parithi's sister's name was Selvi) in hopes that she is Parithi's sister. It turns out that she is not the person whom they were looking for. Catherine suggests that they go to the Census Office to identify Parithi. Murali then gives an idea of painting Parithi as he would look now. They go meet a painter who gets drunk with the money they gave. When his wife sees his drunken stupor, she furiously throws old frames, and Amy identifies one of them to be a photo taken by her. They track down the owner of the image (ChennaiImages.com), which is actually a shooting spot for dramas. They meet the manager, and he says that the pictures were bought in an auction years ago. After they leave, his wife asks him why he lied about the images that his grandfather had saved. Later, it is shown that the man is Nambi's grandson.

Later, Amy falls ill while at her room and is rushed to the hospital. There she meets Parithi's friend, Kabir, in his deathbed. When she inquires about Parithi's whereabouts to Kabir in Tamil, Murali and his assistant get shocked. Kabir breathes his last, saying only the words "Durai Amma", following which he dies soon after. When Murali asks Amy about her knowledge in Tamil and why she did not speak it before, Amy blankly stares at the Cooum River. She narrates her younger days to the three of them.

Following a series of secret meetings between Parithi and Amy, love blossoms between them, and Parithi affectionately calls her "Durai Amma" (lady/female lord), a polite term of addressing British women. However, a major threat comes in the form of independence for India on 15 August 1947, which means that all British white officials and their families, including Amy, would have to leave India. On the eve of independence, all of India is celebrating. However, Amy and Parithi, determined to be together, run away and are hunted by an angry Ellis and his men. An Indian policeman helps the two of them by hiding them in a clock tower on top of the Madras Central Railway Station, but they are discovered by Ellis. After a fierce fight, Ellis is killed, Amy is injured in her head, and Parithi is badly wounded. Amy helps Parithi escape by casting him with a life-raft into the Cooum River, before she is captured and taken back to London. She had never known if Parithi survived or what his fate was.

Back in the present day, Amy is urgently called back to London to have a life-saving operation. However, she is determined to find Parithi and by chance encounters a taxi driver who assumes that she would want to visit a charitable trust named Durai Ammal Foundation. The driver shows her around the foundation, which has organizations providing free housing for orphans and the elderly, medical care, and affordable education (all of which were promised to the dhobi children by the young Amy several years ago). She realizes that the Durai Ammal Foundation was established by Parithi and named after her.

Then, when Amy asks the driver what happened to Parithi, he leads her to his tomb and reveals that he died 12 years ago. She kneels before the tomb and claims the thali (nuptial threads) as her own. She declares "It's mine!" before quietly passing away on Parithi's tomb. Catherine mourns for her, and the taxi driver is dumbfounded to learn that the old woman was "Durai Amma" herself.

The epilogue shows Parithi and Amy (as they were in their younger days) in the afterlife, depicted as a 1940s-style Madrasapattinam. As the credits roll, a series of montage images are shown, illustrating the transformation of the early 20th century Madras into modern-day Chennai.