However, they acknowledge that the British government might find ways to present the various financial agreements it makes in a way it hopes may limit criticism from hardline Brexit supporters of any divorce settlement and transition payments. "We owe it to the people of Northern Ireland and to everyone on the island of Ireland to see through these commitments".
Mrs. May touched on each of those issues, saying London doesn't want to see the return of border between Ireland and Northern Ireland and that British courts will uphold European Union citizens' rights after Brexit.
"The only advance seems to be that the prime minister has listened to Labour and faced up to the reality that Britain needs a transition on the same basic terms to provide stability for businesses and workers".
The EU's chief Brexit negotiator, Michel Barnier, said Thursday that "there is still today major uncertainty on each of the key issues of the first phase".
May also said that European citizens working in Britain will be subject to a registration system during a two-year transition period as Britain withdraws from the EU.
She said the arrangement would give Britain time to implement its departure from the European Union and provide greater certainty to businesses and people. "I'm clear the guarantee giving on your rights is real", she said, adding that a special mechanism needed to be found so that disputes are not left exclusively to United Kingdom courts or the European ones.
Mrs. May also suggested a two-year "implementation period" would be needed after the U.K.'s planned withdrawal in 2019 for both sides to prepare for new trading relations.
Taoiseach Leo Varadkar gave a "cautious welcome" to the speech. He also affirmed that if there were to be a transition period European Union rules and regulations would be applicable during this period.
Speaking from the United Nations in New York, Ireland's foreign minister Simon Coveney said Mrs May's speech was a "positive contribution" but said there was still "a lot of work" to be done.
"The EEA model has also been disposed of, alongside a Canadian-style agreement", he said.
Downing Street had hoped her keenly awaited address would end the stalemate in Brussels and enable the talks to move on to Britain's future relations with the European Union - including a free trade deal.
Rennie's party supports holding a second UK-wide referendum once the final terms of the Brexit deal are known. "Ireland must do the same".
The speech was meant to end the stalemate in negotiations, which are due to resume on Monday 25 September, six months after Article 50 was activated, signalling the UK's intention to leave the EU.