UK employment minister and British Prime Minister David Cameron's Indian Diaspora Champion Priti Patel, Rishi Sunak, the UK-based son-in-law of Infosys chief Narayana Murthy and Suella Fernandes have all signed the letter.
They claimed that Brexit would allow better India-UK trade deals.
"Britain's trade policy is controlled by the EU. That means we are unable to sign bilateral free trade agreements with countries like Pakistan, India, Bangladesh, Australia, New Zealand or for that matter any other non-EU state. Commonwealth countries like India have been in talks with the EU about doing a trade deal since 2007 - to no avail," the letter reads.
"The ancestors of many people we represent fought alongside the British in two world wars, but are now forced to stand aside in favour of people with no connection to the United Kingdom. This is unfair."
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The opposing camp, favouring Britain's membership of the EU, has dismissed claims of better India-UK ties in the event of Brexit.
"We help secure huge amounts of EU development funding for both these countries and many others like South Africa, Sri Lanka and Nigeria. And we continue to push the EU for free trade deal with many Commonwealth countries like Australia and India," he said.
Making a direct appeal to Indian-origin voters, he added: "Many of you have spent years living, working and contributing to the UK. And most of you still have deep ties with India; whether through family, property, or returning to live there again one day.
"Whatever side you come down on, the most important thing is that you have your say. Don't miss the opportunity to vote in this historic moment."
British government officials will be entering a four-week so-called "purdah" period from Friday, which prevents any official activity that could be perceived as an attempt to sway the outcome of the June 23 vote.
It means civil servants will no longer be able to publish reportsin the run-up to referendum day under Electoral Commission rules.