Without directly naming Prime Minister David Cameron or Chancellor George Osborne, she accused them of ignoring the common man.
"It's shameful that those leading the pro-EU campaign fail to care for those who do not have theiradvantages. Their narrow self-interest fails to pay due regard to the interests of the wider public," the British Prime Minister's Indian Diaspora Champion wrote on 'The Daily Telegraph' website.
"Promises have been made that now cannot be delivered. Only a year ago, the Conservative Party's election manifesto pledged to bring net migration down below 100,000 a year... Membership of the EU means that we Conservatives cannot even honour our own promises.
"This only undermines trust in politics and highlights how the EU damages democracy," she wrote.
More From This Section
Her comments came as other Conservative party leaders, including former London mayor Boris Johnson, also called on Cameron to admit defeat over the issue.
(Reopens FGN 11)
Another Tory MP in favour of Brexit, Andrew Bridgen, has also publicly predicted a leadership challenge against the Prime Minister even if he wins the referendum by a narrow margin.
Asked if MPs would demand a leadership contest,Bridgen said: "I think that's probably highly likely. Given the exaggerated claims that the Prime Minister has made, there probably would be 50 colleagues who would be very dissatisfied with the Prime Minister's performance."
"This is a transparent attempt to distract from the fact that the overwhelming majority of economists and businesses believe leaving the single market would be disastrous for jobs, prices and opportunities for people," a Downing Street statement said.
The opinion polls continue to reflect only a slight edge for the Remain camp in the referendum.
A new IPSOS MORI survey of over 600 economists in the UK revealed that 88 per cent of those who replied said leaving the EU single market would damage Britain's growth prospects over the next five years.