The source said Mrs May is "confident" of winning next Thursday's Commons vote.
The newly installed leader of the House of Commons, prominent Brexiteer and former leadership contender for the Conservative Party Andrea Leadsom, said the two-year parliament was essential to pass what has come to be called the "Great Repeal Bill".
"First, we need to get Brexit right".
The decision, taken by the Prime Minister, also means there won't be a Queen's speech in 2018, and that the next one won't take place until after the projected date for Brexit in Summer 2019.
German Foreign Minister Sigmar Gabriel told Sunday's Welt am Sonntag newspaper that "maybe there is now a chance to achieve a so-called "soft Brexit.'" But he said staying in the European Union single market would require Britain to accept European Union workers" freedom of movement.
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The Tories are hoping to secure a supply and confidence arrangement with the Northern Irish party - which has 10 MPs in the new Parliament - whereby the DUP will pledge to back the Government's budget and programme without actually taking up ministerial positions in the administration.
May is promising a government "that consults and listens".
Outside the gates of Westminster Palace the outcry over a deadly tower block fire in a deprived estate nestled in one of London's richest boroughs will manifest in a "Day of Rage" protest which blames the incident on social inequality and years of public spending cuts.
Controversial plans to allow new faith schools to select all of their pupils on the basis of their faith have been abandoned and will be absent from Wednesday's Queen's Speech, it has been reported today.
"It will be very safe and measured Queen's Speech".
Labour, the SNP and the Liberal Democrats all called on Mrs May to use the Queen's Speech to change course, to end austerity and soften her approach to Brexit, but the PM made clear that under her government the country would continue to live within its means and that she would honour the result of the 2016 European Union referendum. Backbenchers have been pushing hard for an enhanced Investigatory Powers Bill in the wake of the recent terror attacks. Additional bills on housing and transport policy are anticipated.