Priti Patel, the senior-most Indian-origin member of Cameron's Cabinet, is part of the 'Leave' camp, which favours "Brexit" or Britain's exit from the EU in the referendum.
"Voting to leave the European Union would be a massive boost to UK-India relations. New opportunities for the UK and India to cooperate more closely and develop stronger trading links would emerge as the UK re-aligns its foreign policy and trade priorities," the 43-year-old employment minister said.
In a statement, she claimed the UK's membership of the EU has acted as a "barrier" to developing trade and investment partnerships and remaining within the EU will mean the UK will be in a "weaker position" to forge the closer trading ties that would benefit the Indian and UK economies.
While praising her Conservative-led government for enhancing the UK's ties with "dynamic and fast-growing" India, she stressed that things could go much further if the UK was not held back by the "vested self-interests of the EU".
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"Indeed, one of the reasons why our trading links with India were inadequate when we came to Government in 2010 was because of the focus that Britain had given to trade within Europe as a result of membership of the EU," she said.
She said: "During the forthcoming referendum the Indian diaspora can vote to make a real and positive difference to the future of the UK and India by voting to leave the EU.
"Because we are unable to restrict migration from the EU, immigrants from non-EU countries have faced more restrictions to help ease the pressure from immigration. I know that many members of the Indian diaspora find it deeply unfair that other EU nationals effectively get special treatment. This can and will change if Britain leaves the EU."
"The diaspora have a great reputation as business owners and entrepreneurs. However, like all businesses, they have been hit hard by bureaucracy, red tape and regulations from the EU."
Her comments are in contrast to Cameron's own assertion in Parliament yesterday that the UK could lose its "negotiating muscle" in future trade deals with countries like India in the event of Brexit.
The campaign for and against Britain's membership of the EU is gathering momentum and a large number of UK companies today issued a letter warning against the economic impact of Brexit.
In the letter to 'The Times' newspaper,about 200 business leaders employing more than 1.2 million people backed Cameron's call that Brexit would put jobs at risk.
"Business needs unrestricted access to the European market of 500 million people in order to continue to grow, invest and create jobs. We believe that leaving the EU would deter investment and threaten jobs. It would put the economy at risk," reads the letter backed by the likes of Vodafone, Marks & Spencer and British Telecom.
However, the "Leave" camp dismissed this clarion call as not representing a large enough number of well-known businesses, with supermarket chains Tesco and Sainsbury remaining politically neutral.
Meanwhile, a change to the UK's Civil Service Code means that British civil servants have been banned from helping ministers make the case for leaving the EU.
They will, however, be allowed to help ministers arguing for Britain to remain in a reformed EU, according to Downing Street.
The government's official policy is that Britain should remain in the EU and civil servants are said to be duty bound to support government policies.
The UK Cabinet is split over the issue with 17 members in favour of staying in the EU and five wanting to leave.
The ruling Conservative party MPs are also split - 142 to 120 in favour of staying.
"I have huge respect for Boris as a politician and he is a great friend of mine, and he is a fantastic mayor of London. I think he has a lot to give to the Conservative party and to this country, but on this issue I think he has got it wrong and reached the wrong conclusion," Cameron said in reference to London mayor Boris Johnson favouring Brexit.