The Conservative manifesto also said welfare payments for older people would be cut to fund social care and free school provision would be reduced to boost investment in other parts of the education system.
If she wins on June 8, May will have one of the toughest jobs of any recent British prime minister: holding the United Kingdom and its economy together while conducting arduous divorce talks with European Union leaders on the intricacies of finance, trade, security and immigration.
Sir Michael said it would become easier to reduce migration as the United Kingdom leaves the European Union and pointed to another manifesto pledge, to increase the levy on firms hiring foreign workers.
May said she stood within the mainstream of Conservative party thought, rejecting suggestions she had a distinctive personal approach or wanted to be compared with Thatcher.
Paul Johnson, director of think tank the Institute for Fiscal Studies, said sharply reducing immigration would be "an additional cost on employers and the economy" because it implied losing a source of productive labor.
"There is no Mayism. There is good solid Conservatism, which puts the interests of the country and the interests of ordinary working people at the heart of everything we do in government", she said at a news conference to launch the Conservatives' policy pledges before a national election she called for June. Sir Andrew Dilnot, first recommended that people pay no more than £35,000 for their social care in his report to the Coalition Government in 2011 and has expressed his dismay over the absence of a social care cap.
Her manifesto states: "no matter how large the cost of care turns out to be, people will always retain at least £100,000 of their savings and assets, including value in the family home".More news: Penguins turn to Matt Murray for Game 4 of Eastern final
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Mr Corbyn will say: "Where the Tories look to divide, Labour seeks to bring people together".
On Thursday, Theresa May announced that the universal £30 winter fuel allowance would become means-tested, stripping the money from an estimated 10m pensioners.
"Every vote for me and my team will strengthen my hand in the negotiations to come", May said at the launch in Halifax in northern England, calling it "a manifesto to see us through Brexit and beyond".
"The next five years will be the most challenging that Britain has faced in my lifetime", she wrote in The Telegraph newspaper. A plan for a stronger, fairer, more prosperous Britain. "Brexit will define us - our place in the world, our economic security and our future prosperity".
Mrs May said she was maintaining Mr Cameron's controversial target to reduce net immigration below 100,000 - something she failed to do in six years as home secretary.
The triple-lock, which guarantees pensions rise by the highest of average earnings, inflation or 2.5 per cent, will be replaced by a so-called "double-lock", with the figure of 2.5 per cent dropped from the equation.