European Council president Donald Tusk has warned there can be "no frictionless trade" with the EU if the UK is outside the customs union and single market.
"Friction is an inevitable side effect of Brexit by nature," he told business leaders in Brussels.
A "hard border on the island of Ireland" is one of the "possible negative consequences" of the kind of Brexit set out by the UK's red lines, Donald Tusk said.
The European Council president said he would ask Theresa May at their meeting in London whether the UK has "a better idea that would be as effective in preventing a hard border" as that set out in Brussels' draft withdrawal agreement - which has been rejected as unacceptable by the Prime Minister.
Meanwhile, Irish senator Neale Richmond, European affairs spokesman for the Fine Gael party that leads the Government, said Britain has provided "zero detail" on its proposed alternatives to keeping Northern Ireland in a customs area with the EU to avoid a hard border with the Republic of Ireland.
He told BBC Radio 4's Today programme: "We are very, very hopeful that an overarching, overall trading and customs agreement (for the whole UK) can be reached.
"However the British Government has stressed there are alternative options and imaginative options, that's well and good and fine and the European side, we are of course prepared to look at that, but we have seen zero detail about those."
Mr Richmond also dismissed Boris Johnson's suggestion that crossing the Irish border could be managed in a similar way to the congestion charge in London, without the need for physical checks.
"You are talking about two boroughs that are in the same customs union, that are in the single market, that didn't have an armed conflict in the last 20 years - it is an absolutely ridiculous suggestion that is not comparable to the situation on the island of Ireland," he said.
Ireland's EU Commssioner Phil Hogan criticised Boris Johnson for remarks he made earlier in the week about the Irish border question.
Responding to his comparison to the congestion charge in London, Mr Hogan said: "People like Boris Johnson, he has belittled the importance of the Good Friday Agreement ... by comparing the type of solution to the border issue as similar to a congestion charge between two London boroughs.
"He is not the mayor of a London borough, he is actually the Foreign Secretary of the United Kingdom of Great Britain and Northern Ireland and I think he should know his place."
Mr Hogan told RTE Radio One's Sean O'Rourke Show that it was very frustrating trying to deal with a divided British Government.
"Rather than red lines that we have seen accentuated from the beginning of this process, we need clear lines," he said.
Arriving at Downing Street for talks Mr Tusk told the PM: "I'm absolutely sure that after your so-called red line, we'll I'm not happy with it, you know, but of course, but it's natural that you have maybe different point of views when it comes to the essence of Brexit.
"Anyway, after your decision on no customs union and no single market it's some kind of breakthrough and we can start our substantive negotiations immediately."