And Ms Soubry - a leading figure in the Remain campaign before last year's European Union referendum - told the BBC's Sunday Politics programme that Mrs May would have to listen to businesses and "wise owls" in her government who are calling for the single market to be a priority over immigration curbs.
May called for a snap election in April so her Conservative party could widen its majority in Parliament.
Defense Secretary Michael Fallon, a member of May's Conservative party, told the BBC: "What we do have now is an understanding of the outline proposals that would underpin that working agreement".
DUP MPs are meeting to discuss the situation and one told Sky's Senior Political Correspondent Beth Rigby earlier: "We would consider a supply and confidence arrangement to make sure Theresa May has sufficient support to keep her in government".
Principal among them is Scottish Conservatives leader Ruth Davidson who, having helped her party win 13 seats in Scotland, has already expressed her concerns about the DUP's attitudes to homosexuality and women's rights.
Shortly after her comments Downing Street confirmed that five high-profile Cabinet ministers would remain in place. And the Brexit talks are due to start in 10 days time.
Sterling fell broadly on Monday as investors anxious about the impact of a period of political uncertainty on an economy already slowing sharply ahead of the launch of talks on leaving the European Union next week.
He added, "I don't think Theresa May and this government have any credibility".
Britain has a hung parliament after the Conservatives lost their majority on an extraordinary night.
British Prime Minister Theresa May's two chief advisers announced their resignation Saturday after a crushing electoral setback left her Conservative party in disarray and the country without a clear mandate.
As a leader of a minority government, May will be forced to adopt a more consensus based approach, and this could lead her vulnerable to rivals within the party, should Brexit negotiations run into difficulty.
"This is not the time for sharks to be circling". I think she will have to go unfortunately.
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"I have no doubt at all that Theresa May will continue to serve and work hard as Prime Minister - and do it brilliantly".
The DUP is similar to the "religious right" in the USA and takes a hard-line stance on social issues, such as same-sex marriage and abortion.
Even if May remains at the helm of the next government, she will have to negotiate a Brexit agreement that will have little chance of getting through the House of Commons, as all other parties (including even Northern Ireland's Democratic Unionist Party, on which her next government would have to rely) want a relatively soft Brexit.
DUP Leader Arlene Foster recently denied the party was homophobic.
"Just to be clear, we will act in the national interest".
It was also likely to seek to include Northern Ireland in the "Military Covenant", which ensures that veterans of the British armed forces receive priority medical treatment in the remainder of the United Kingdom.
Ex-chancellor George Osborne said the DUP's position made Ms May's "central claim" - that no deal is better than a bad deal - "undeliverable". "We do not agree and we do not have to agree with any of their views on these social issues and I certainly don't".
"I can still be prime minister", Corbyn said.
Damian Green, the former work and pensions secretary, was named first secretary of state - effectively the deputy prime minister.
"A handful of senior people have pledged their loyalty to Boris at Cabinet level", a Johnson ally told The Sunday Times. However, her government may lack the support for such an endeavour during negotiations.
He said there was a "possibility" of voting down the Queen's Speech and Labour were going to "push all the way" to achieve that.





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