Booker Prize winner Rushdie, recent Booker prize shortlisted British-Indian author Mukherjee and other well- known names like Ian McEwan and Hari Kunzru are among the signatories of an open letter to Cameron.
"We, the undersigned, are extremely concerned about the rising climate of fear, growing intolerance and violence towards critical voices who challenge orthodoxy or fundamentalism in India... We urge you to engage with Prime Minister Modi both publicly and privately on this crucial issue," the letter says.
The letter was published by PEN International - a worldwide membership organisation for prominent literary figures, and signed by members of its centres in England, Wales and Scotland.
It points to the recent murders of the intellectuals Malleshappa Madivalappa Kalburgi, Govind Pansare and Narendra Dabholkar, and to the protests that have seen at least40 Indian writers return literary awards to the Sahitya Akademi, the National Academy of Letters, in condemnation of its silence over the attacks.
"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."
Carles Torner, executive director of PEN International, said: "Prime Minister Modi's visit to the UK is an opportunity... To ensure that the disturbing trend of intolerance towards dissent and criticism in India is raised.