Instead, after a botched campaign focussed entirely on May, the Conservative Party lost its majority in last Thursday's election.
Even without the impact of the London fire, the talks were said to be making "slower progress".
The move comes amid concerns the Government will compromise its stated impartiality in the region if it enters a confidence and supply deal with the DUP at Westminster.
Last night, Downing Street sources would only say talks were "going well".
The Conservative source said talks with the small Northern Irish party were progressing well ahead of meetings later Thursday in Downing Street with all of the British province's main political leaders.
However, sources close to the talks said that while the discussions were "stuttering", 95% had been agreed between both sides, meaning the deal could still be announced in time to allow the Queens's speech on Monday.
Earlier in the week ministers had already said the Queen's Speech was likely to be set back from its scheduled date of Monday June 19, because of ongoing negotiations.
DUP leader Arlene Foster, who travelled to Westminster for talks with the Tories on Tuesday, said she hoped a deal could be reached "sooner rather than later".
Lions coach Gatland rails at New Zealand 'blocking'
The Wales flanker has struggled for fitness in the opening weeks of the tour and played in only two of their five warm-up matches. New Zealand commentators have condemned the Lions as boring and have criticized the one-dimensional nature of their game plan.
"We never put timescales on when we expect a deal to be done and I'm not going to start now".
Jeremy Corbyn, leader of the opposition Labour Party, which saw its number seats and share of the vote increase, said there could be another election this year or early in 2018 after last Thursday's vote produced no clear victor.
Brexit minister David Davis has insisted the approach to the European Union divorce has not changed, but May has recognised that a broader consensus needs to be built for Brexit and has made clear she would listen to all wings of the party on the issue.
"I think there will be pressure for a softer Brexit", Mr Cameron added, saying that Parliament "deserves a say" on the issue.
"Look at what the Tories (Conservatives) have managed to do to the United Kingdom in the space of just one year, firstly calling a divisive and reckless European Union referendum. then having lost that gamble pursuing a hard Brexit path", Scotland's first minister, Nicola Sturgeon, said.
With formal European Union divorce talks due next week, May heads to France on Tuesday, possibly to bask in the popularity of Emmanuel Macron, who last month swept to victory in a presidential contest.
France's Macron said the EU's door was still open for Britain as long as the negotiations were not finished, but that it would be hard to reverse course.
"We are steadfast in our commitment to devolution and are ready to work with all willing partners to restore the devolved institutions in the interests of all our people".
"I congratulate her on returning and I'm sure she'll agree with me that democracy is a wondrous thing, and can throw up some very unexpected results", he said.