"The union as I've said before is our guiding star", she said.
Theresa May could continue to lead a minority government or she can get a small majority with the help of the DUP.
"It may not be on the Monday because we also have got the Queen's Speech that week and I will have to speak in that, and so on".
Speaking on ITV's Good Morning Britain, Mr Brady said the overriding mood within the Conservative Party was one of realism and recognising they had not got the result they wanted.
It was a surprise move - Gove was sacked as justice minister by May previous year after his bid to become party leader forced now-Foreign Minister Boris Johnson from the race, amid accusations of treachery and political backstabbing.
But Osborne, who is now the editor of London's Evening Standard newspaper, downplayed the prospect.
"The reason for leaving the single market is because we want to take back control of our borders, they're not compatible", he told BBC radio.
"In order to deliver that you can't do that inside the single market, so what do you do, you try and have the best possible access from outside".
The DUP voted to leave the EU, Meban said, but they're "very conscious" of this unique relationship and they're unlikely to do anything that would be detrimental to the economy of Northern Ireland.
The uncertainty about the speech laying out the government's legislative program comes as May conducts talks with the Democratic Unionist Party, which is certain to expect concessions for its support.
For now, though, Prime Minister May's keeping her stiff upper lip and pushing ahead.
One of the biggest cheers during the meeting came for the "greatly respected" Gavin Barwell, Mrs May's new chief of staff who will have a "great deal of influence" alongside Chief Whip Gavin Williamson in the new Government.
May called the early election in April when opinion polls suggested she was set for a sweeping win which would give her a strong mandate to start Brexit talks with the EU.
Britain's Prime Minister Theresa May and her husband Phillip arrive at church in Sonning, Britain June 11, 2017. Still, it was a step made inevitable by her desperate need to shore up the government's support base.
Defense Secretary Michael Fallon said on the Andrew Marr show he believed the Conservative Party and the DUP will be able to hold together in government.
There are fears among more liberal Conservative MPs that the socially conservative DUP will demand a scaling back of abortion and gay rights - but No. 10 sources have insisted these issues are not on the table.
Damian Green, a lawmaker in the pro-EU wing of the party, was promoted to first secretary of state - effectively deputy prime minister. Many key positions were unchanged. Gove, a long-time opponent who was dismissed when May became prime minister past year, will now serve as environment secretary.
They are lobbying for the government to negotiate a much closer relationship with the European Union than previously planned by the embattled May, who appears determined to cling to power, at least in the short term, in the face of fury in the party over last week's election result. May said that he would bring "considerable experience" to the post.
May on Sunday unveiled her full cabinet, which will meet for the first time on Monday, making few changes as she vowed to cling on despite pressure to quit. "Let's get on with the job".
The Prime Minister was doing her utmost to signal that it was business as usual, announcing that she would be heading off to Paris on Tuesday for talks with French president Emmanuel Macron.
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