Talks with the DUP on a deal to shore up a minority Conservative administration are "progressing well" and the parties have reached "broad agreement" on the principles of the Speech, which will set out the Government's legislative programme for the coming year, according to a senior Conservative source.
Theresa May should agree to pay Britain's bills to the European Union and drop threats to walk out without a legal deal if she wants talks on the "softer Brexit" some of her allies are calling for, EU negotiators say.
On Tuesday May, following a meeting with French President Emmanuel Macron in Paris, reiterated her government will get on with Brexit and make a success of it. She also said that the talks with May's party had covered corporation tax and same sex marriage.
A lackluster campaign saw her high approval rating slip away, and support for her "hard Brexit" strategy-pulling out of the European single market and customs union-now hangs in the balance.
Major said taking the unionists party into a British coalition government could imperil the accords.
"The risk is that Northern Ireland continues to fail to find solutions, and potentially the peace process unwinds", he told AFP.
London's neutrality is key to the delicate balance of power in Northern Ireland, which was once plagued by violence over Britain's control of the province.
The Prime Minister will meet separately with representatives of Sinn Fein, the Ulster Unionists, the SDLP and the Alliance Party - as well as the DUP - in Downing Street in an attempt to allay growing concerns.
"This new arrangement is very unsettling and people are concerned and anxious about what it may mean, or what promises may be given".
Meanwhile, the EU and United Kingdom government confirmed that Brexit Secretary David Davis and European Commission chief negotiator Michel Barnier will meet in Brussels on Monday.
"It's passing quicker than anyone believes..."
"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 will be making it very clear that any deal between the Tories and the DUP can not be allowed to undermine the Good Friday and subsequent agreements". But a newly appointed junior Brexit minister, Steve Baker, told Reuters: "I don't foresee any change ..."
Nigel Farage, former head of the eurosceptic UK Independence Party, admitted that after May's election disaster Britain is in a "very weak" negotiating position.
Uncertainty over Brexit has already had a "negative impact on everybody in Europe, especially on Britain", said Mr Verhofstadt.
Demanding a swift start to Brexit negotiations under Article 50 of the European Union treaties, the former Belgian prime minister compared Britain's position to the heroine of Lewis Carroll's Alice In Wonderland, who found herself in a room with many doors and no idea what lay behind them. It is the only way to unite the country and strengthen our bargaining power with the EU.