An open letter has been published by Pen International as Mr Modi flies into the UK for a three-day visit.
The writers have expressed concern over the "growing intolerance and violence towards critical voices" in India.
They want to urge Mr Modi to "safeguard freedom of expression".
The letter has been signed by hundreds of members and supporters of Pen International's centres in England, Scotland and Wales, including Nikita Lalwani, Henry Marsh, Hari Kunzru, Neel Mukherjee and Owen Sheers.
It urges the British prime minister to raise the "crucial" issue with Mr Modi both "publicly and privately" during his visit, where plans include addressing parliament, visiting the Queen and staying at Chequers.
The letter highlights threats made to writers who have "challenged orthodoxy or fundamentalism in India", and the murders of three intellectuals - Malleshappa Madivalappa Kalburgi, Govind Pansare and Narendra Dabholkar - in the last two years.
Recently at least 40 Indian novelists, poets and playwrights have returned prizes awarded by India's National Academy of Letters in protest over the organisation's silence on the attacks.
They criticised the academy's failure to speak up and challenge the government to "demonstrate tolerance and protect free speech" and the "deteriorating political environment in which those expressing dissent have been attacked by government ministers".
The letter concludes: "In line with the United Kingdom's stated commitment to promoting human rights, we ask that you raise the above issues with Prime Minister Modi and urge him to provide better protection for writers, artists and other critical voices and ensure that freedom of speech is safeguarded.
"Without these protections a democratic, peaceful society is not possible."
Downing Street has yet to respond to a request for comment on the letter.
More than 200 writers including Salman Rushdie, Val McDermid and Ian McEwan have called on David Cameron to address India's "rising climate of fear" with its Prime Minister Narendra Modi.