Brussels’ chief Brexit negotiator Michel Barnier has welcomed the “clarity” from Theresa May over her plans for future UK-EU relations.
He said her position on the single market, customs union and the “recognition of trade-offs” would inform the guidelines on the free-trade agreement for the European Council.
But senior German MEP Manfred Weber said he was “even more concerned” about reaching a Brexit deal after the speech.
Mr Weber, chairman of the centre-right EPP group in the European Parliament and an ally of Angela Merkel said: “After what I have heard today I am even more concerned.
“I don’t see how we could reach an agreement on Brexit if the UK government continues to bury its head in the sand like this.”
Business leaders welcomed elements of the speech – but called for more details.
CBI director general Carolyn Fairbairn said: “We heard the strongest acknowledgement yet of what’s needed to get a good deal.
“A possible future role for the ECJ, membership of some EU agencies, willingness to take steps to guarantee a level playing field – these are all welcome softening of red lines.”
But she called for more work to “lift the fog of uncertainty”, saying it was vital to reach a deal on transition by the end of the month.
While the Government had “moved in the right direction” on alignment with EU rules in some areas, sectors including food and drink had been “left on the sidelines”.
And Mrs May’s proposals on customs “do not deliver” on the goals of frictionless trade and avoiding a hardening of the Irish border.
Stephen Martin, director general of the Institute of Directors, said: “Business leaders will welcome the Prime Minister’s honest admission that negotiating the future UK-EU relationship will involve making difficult choices.”
But he also raised concerns about customs, adding: “It is important to stress that if the UK is doubling down on its unprecedented customs partnership model, HMRC have said it will take five years minimum to implement.
“That means businesses will need longer to adjust to new settings.”
DUP leader Arlene Foster said: “I welcome the Prime Minister’s clear commitment that she will not countenance any new border being created in the Irish Sea between Northern Ireland and the rest of the United Kingdom.
“Northern Ireland goods must have unfettered access to trade into Great Britain and the same must apply to Great Britain goods entering Northern Ireland.
“Indeed, it is particularly welcome that one of the ‘five tests’ is strengthening the union.”
Liberal Democrat leader Sir Vince Cable said Mrs May had outlined all the reasons why we should stay in the single market and customs union “but she will carry on regardless”.
“May’s diminished authority is allowing Brexit extremists to neuter any chance she has at getting an acceptable deal for the UK,” he said.
Interim Ukip leader Gerard Batten said Mrs May’s five tests were “aspirational waffle” and “what she is delivering is not Brexit, but the possibility of future Brexit”.
Labour MP Peter Kyle, a supporter of the pro-EU Open Britain campaign said: “The Prime Minister said she wanted to present some ‘hard truths’: what we got was a list of reasons why Brexit is much more complicated, much more difficult and much more costly than anyone could have known about during the referendum.
“With that in mind, everyone is entitled to keep an open mind about whether it’s the right path for the country.”