But Jeremy Corbyn, leader of Britain's main opposition, said his Labour Party would not support May's Queen's Speech in the lower house of parliament to try to force her out of power through a vote of no confidence.
One of the more significant meetings being held is that of Theresa May with the Sinn Fein President Gerry Adams which is said to be taking place this afternoon.
Before the Mansion House dinner was cancelled because of the fire, finance minister Hammond had been due to tackle fears among the financial elite that May's insistence that "no deal is better than a bad deal" would cost them business.
"We remain fully committed to making the institutions work", she said.
Mrs Foster, who travelled to Westminster for talks with the Tories on Tuesday, said she hoped a deal could be reached sooner rather than later. Since the surprise result, much media attention has focused on the DUP's policy lines on social issues, with the party being strongly socially conservative, promoting a type of rhetoric around gendered rights in particular which is in stark contrast to the liberal, compassionate Conservatism that former PM David Cameron championed.More news: Turkey's Erdogan slams 'inhumane' isolation of Qatar
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Speaking as talks continued between Number 10 and the Northern Irish party, Mr Hanson - who was returned as an MP for the seventh time in last week's General Election - said the group led by Arlene Foster would not give an inch during the ongoing dialogue.
Discussions broke up on Tuesday night without an agreement, but Mrs May said that they had been "productive".
She added: "Progress will not come from a deal between the DUP and Tories to prop up a Government in Westminster with an austerity and Brexit agenda but through the full implementation of the agreements and an Executive that respects the rights and delivers for all in society".
"We will go into speak with Sinn Féin again on Monday morning because devolution works and works for everybody in Northern Ireland", she said emphatically.
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. The turbulent period in British politics that begun in the wake of the Brexit vote last June, looks set to continue.
"There is an irony to being lectured by some about our role in the national government of the United Kingdom when Sinn Féin want to be in government here in the Republic of Ireland", she said.