After days of political turmoil sparked by her botched gamble on a snap election, May's Conservative Party resumed talks with a small Northern Irish Protestant party on securing the support of its 10 members of parliament to pass legislation.
The source said talks with the small Northern Irish party were progressing well as meetings in Downing Street with all of the British province's main political leaders were taking place.
Northern Ireland's largest nationalist party Sinn Fein said it would oppose any deal that undermines a peace deal known as the Good Friday Agreement, with President Gerry Adams telling Britain: "We want to govern ourselves".
And since the election results last week that left Prime Minister Theresa May without a parliamentary majority, that chaos and confusion have intensified.
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.
Ms O'Neill said: "We made very clear the the Prime Minister that any deal between herself and the DUP can not undermine the Good Friday Agreement, it can not undermine the joint nature of the office".
The loss of her majority meant May has been reaching out to the ultra-conservative Democratic Unionist Party to prop up her Conservative party.
The start of Brexit negotiations next week will focus on European Union citizens' rights, the UK's divorce bill and Northern Ireland's border.
He said he emphasised to Mrs May that his party stood ready to form a new executive "without any preconditions or red lines".
But May's predecessor, David Cameron, said there would be pressure after last week's surprise for a "softer" Brexit that gave greater priority to a close trading deal with the EU.
Even some Republicans have grudgingly admitted if this investment is forthcoming from the central government in London it could be a good thing for Northern Ireland.
"A little side bargain to keep Theresa May in power. won't have any integrity and certainly isn't as important as the needs of people" in Northern Ireland, said Adams.
On Brexit, Ms Foster said her party wanted to see "a sensible Brexit and one that works for everybody".
Brussels has insisted talks on the so-called divorce, taking in issues including the fee the United Kingdom will have to pay to sever its ties, must make sufficient progress before any discussion on a future trade agreement could begin.
"As we enter negotiations next week we will do so in a spirit of honest cooperation, taking a pragmatic approach, trying to find a solution that works" for Britain and the European Union, he said.
Speaking as he arrived for a meeting of European Union finance ministers in Luxembourg, he said: "As we go into that negotiation, my clear view - and I believe the view of the majority of people in Britain - is that we should prioritise protecting jobs, protecting economic growth and protecting prosperity as we enter those negotiations and take them forward".
Whatever her ultimate plan, she will be heavily reliant upon the ten lawmakers from the eurosceptic DUP, who would help her edge past the 326 votes needed in parliament to avoid the government collapsing.