However, it faces the prospect of delivering a Queen's speech while still thrashing out a deal with Northern Ireland's Democratic Unionist Party.
So far, he has been successful in that job, making clear the European single market's "four freedoms", including free movement, are indivisible and forcing Mrs May to confirm her intention to pull the United Kingdom out to get control of immigration.
But EU officials are sceptical that May's position has changed, just as they are doubtful about the feasibility of either option. "It continues and when the deal is done, it will be done", a senior source in the Conservative Party said yesterday.
At one of the most important junctures for Europe and the West since the 1991 fall of the Soviet Union, May's government is reeling from a crisis of her own making - the loss of her parliamentary majority in a June 8 snap election she did not need to call.
Only 35% of respondents agreed with the Prime Minister's strategy.
"I will spare no effort to fulfil the Government's duty as co-guarantor of the Good Friday Agreement".
Her failure to win a majority has put May under pressure over her Brexit plans from inside and outside her party and has prompted complaints about her choice of partner due to the DUP's stance on social issues such as gay marriage and abortion.
"When I talk about a Brexit that supports British jobs, British investment and British business I mean a Brexit that avoids those cliff edges", Hammond said in an interview with BBC television.
Andrea Leadsom, leader of the House of Commons, said that Brexit would require a lot of legislation, including a law to enshrine current European Union rules into British law, known as the "Great Repeal Bill".
The Irish government statement said there was agreement on the importance of a functioning executive in the context of the Brexit negotiations due to start next week.
DUP leader Arlene Foster said a year ago that advocates of same-sex marriage were likely to send her "in the opposite direction", while Ian Paisley Jr, the son of DUP founder Ian Paisley, has called homosexuality "immoral, offensive and obnoxious".
"We know each other and we understand each other", she said.
May's programme will most probably have to be watered down, dropping some of her preferred reforms to help get legislation through Parliament and possibly having to give way to other ministers who have strong views over the direction of Brexit.
Three days after the talks begin, May is due to travel to Brussels for an European Union summit - a chance for the other 27 leaders to take stock of their negotiating partner in the sharply altered climate brought about by the dramas of the past two weeks.