The 105-carat stone, believed to have been mined in India nearly 800 years ago, was presented to Queen Victoria during the Raj and is now set in a crown belonging to the Queen's mother on public display in the Tower of London.
David de Souza, co-founder of the Indian leisure group Titos, is helping to fund the new legal action and has instructed British lawyers to begin High Court proceedings.
"The Koh-i-Noor is one of the many artefacts taken from India under dubious circumstances. Colonisation did not only rob our people of wealth, it destroyed the country's psyche itself.
"It brutalised society, traces of which linger on today in the form of mass poverty, lack of education and a host of other factors," De Souza told 'Sunday Telegraph'.
The legal action coincides with Prime Minister Narendra Modi's visit to the UK this week, which includes a lunch hosted by the Queen at Buckingham Palace.
The Koh-i-Noor, which means "mountain of light", was once the largest cut diamond in the world and had been passed down from one ruling dynasty to another in India.
But after the British colonisation of the Punjab in 1849, the Marquess of Dalhousie, the British governor-general, arranged for it to be presented to Queen Victoria.
The last Sikh ruler, Duleep Singh, a 13-year-old boy, was made to travel to Britainin 1850 when he handed the gem to Queen Victoria.
The British law firm instructed by the campaigners, calling themselves the Mountain of Light group, told the newspaper it would be basing its case on principles enshrined in British law that give institutions the power to return stolen art.
Bhumika Singh, a Bollywood actress backing the campaign, said: "Koh-i-Noor is not just a 105-carat piece of stone. It has a lot of history and culture attached to it, and undoubtedly should be returned to India."
The campaign has found support in Britain with the likes of Labour party Indian-origin Labour MP Keith Vaz, who said: "What a wonderful moment it would be, if when PM Modi finishes his visit, he returns to India with the promise of the diamond's return."
The British government has previously rejected all demands for the return of Koh-i-Noor, and in 2013 British Prime MinisterDavid Cameron while on a visit to India, defended Britain's right to keep it saying he did not believe in "returnism".
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