The prediction about the Conservative Party’s fate comes from a model made by Lord Michael Ashcroft.
It shows Mrs May's likely majority has declined from a week ago but estimates she will still increase her majority to 60 seats.
The model predicts the Conservative Party will win 355 seats in the 650 seat parliament.
May is on track to win a majority of 60 seats in parliament, a poll by Lord Ashcroft shows
Lord Ashcroft, a Tory donor, said: "This week's estimates from the Ashcroft Model suggest a narrowing of the Conservative majority, though still a comfortable victory for Theresa May.
"The majority could be considerably better or worse than this for the Conservatives, depending on the pattern of turnout.”
But much hangs on turnout, with the estimated Tory majority falling to 40 seats if all of those who voted in the 2016 EU referendum cast their ballots, and rising to 78 if only those who voted in 2015 take part.
The model predicts the Conservative Party will win 355 seats in the 650 seat parliament
The Ashcroft model brings together large-scale surveys and detailed census data to try to understand what is happening in individual constituencies.
It comes as the Prime Minister’s lead narrows with less than a week before polling day on Thursday June 8.
The latest Ipsos MORI poll says Mrs May's Conservatives now lead the opposition Labour Party by just five percentage points, down from 15 just over two weeks ago.
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The race tightened as Labour leader Jeremy Corbyn went on the charm offensive
The Ipsos MORI poll put the Conservatives on 45 per cent, down four points from a comparable survey on May 18, with Labour up six points to 40 percent.
Ben Page, chief executive of Ipsos MORI, said: “It is clear that on contact with the voters, Mrs May is not going down well and she is losing ground in particular amongst middle aged voters and female voters.”
Mr Page said that Labour's share of the vote included many younger voters who had not voted before.
"Even with all those young people who say they are going to vote and may not, Mrs May should still win a majority so I wouldn't sell your pounds yet," Page said.
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Mrs May hopes the election will strengthen her hand ahead of Brexit negotiations but the race has tightened this week as Labour leader Jeremy Corbyn goes on the charm offensive and seized the opportunity to attack Mrs May after she refuse to go head-to-head in a leaders debate.
The Ipsos MORI poll found Mrs May's personal ratings had fallen, although she still holds a 15-point lead over Mr Corbyn on who would make the better prime minister.
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A failure to win the June 8 election with a large majority would weaken Mrs May just as Brexit talks are due to begin.
Against the Bank of England's trade-weighted basket, which measures sterling's broader strength, the pound is now back where it was on April 9, before May called the election.
Scotland's First Minister Nicola Sturgeon said while Mrs May was no longer certain of increasing her parliamentary majority, she was sceptical about suggestions the Conservatives would lose their current slim majority.
She said: “The most likely outcome here is a Tory (Conservative) victory, but a Tory victory no longer certain of an increased majority.”