Conservative former Prime Minister Sir John, who was crucial in bringing peace to Northern Ireland, raised concerns about the impact of a Tory deal with the DUP. "We need to hope for the best but prepare for the worst".
May will host Arlene Foster in Downing Street to discuss terms of the DUP's backing for her minority government, reports the BBC.
After losing her parliamentary majority in a botched gamble on a snap election, May is so weakened that her Brexit strategy has become the subject of public debate inside her own party, with calls for her to take a more business-friendly approach.Seeking to avoid a second election that could deepen Britain's worst political turmoil since last June's shock vote to leave the EU, May edged closer to a deal to win the support of the Democratic Unionist Party (DUP).She held talks with DUP leader Arlene Foster, whose eurosceptic Northern Irish party has 10 parliamentary seats and could shore up May's minority Conservative government."What we're doing in relation to the talks that we're holding, the productive talks we're holding with the Democratic Unionist Party, is ensuring that it is possible to, with their support, give the stability to the United Kingdom government that I think is necessary at this time", May told a news conference in Paris following a meeting with French President Emmanuel Macron. During the election campaign, May had used the "coalition of chaos" phrase to describe what a victory for Labour would look like.
May is under pressure to take on a more cross-party approach to Brexit talks.
It comes after the Prime Minister apologised to her MPs for the election result, telling them: I got us into this mess and I will get us out of it. The Evening Standard, edited by ex-Treasury chief George Osborne, reported that Cabinet ministers have initiated talks with Labour lawmakers to come up with a "softer", less hard-line divorce from the EU.
In an article for the Times on Tuesday, the new Environment Secretary Michael Gove - who has clashed with May in the past - said she was the ideal person to secure a Brexit agreement that "commanded the widest possible support" given her track record of "seeing through vital jobs to the end".
"The parliamentary arithmetic is such that we are going to have to work with everyone", he said.
It is thought Mrs Foster, despite being a Brexit supporter, could seek assurances from Mrs May that she will pursue a softer exit from the European Union, given the North's 56% Remain vote and the DUP's desire not to see a return to a hard border with Ireland.
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Foster will nearly certainly ask for greater investment in Northern Ireland as part of the deal, as well as guarantees on support for pension plans and for winter fuel allowances for older people.
Even the idea of an alliance is complicated, however.
May now stands accused of throwing the peace process into jeopardy by forming an alliance with the DUP at a time when London and Dublin are supposed to be neutral in finding a way to break the impasse of the forming of a Northern Ireland Executive.
Foster's rivals in Northern Ireland, such as Sinn Fein's Gerry Adams, have objected.
In the briefing they said the prospect of an agreement between the Conservative Party and the DUP was causing "anxiety and fear" over fears that any deal agreed on would affect issues relating to Northern Ireland.
The stakes for May are high. Without a so-called confidence and supply deal with the DUP, her party risks losing the vote next week on the Queen's Speech, which lays out the agenda for the government. If that happens, Corbyn will demand a chance to try to form a government by uniting progressive factors in the House of Commons.
Meanwhile, the chief European Union negotiator has told the Financial Times that Britain that the clock was ticking on Brexit talks, and that Britain should be wary of further delays. "I can't negotiate with myself".
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