Britain must give Brussels a clear Brexit blueprint to allow negotiations to move forward, according to the European Union chief leading the exit talks.
All those involved "know where the EU stands" but "more clarity" is still needed from the UK, Michel Barnier said.
In a speech in Hannover, he said it was up to the Government to come up with its vision for the future that either finalised or changed the UK's red lines.
"It is now up to the UK to come up with its vision for the future, which should confirm the UK's red lines or adapt them," he said.
"Once we have more clarity from the UK, we will prepare a political declaration on the framework for the future relationship to accompany the withdrawal agreement in the autumn."
It comes as the UK Government suffered three more heavy defeats in the House of Lords over its flagship Brexit legislation.
In the main reverse, peers backed a cross-party move to retain key EU human rights provisions on exiting the union.
Earlier, Theresa May was forced to again insist the UK must leave the customs union after Brexit in order to strike trade deals around the world after a massive defeat on the issue in the Lords previously.
Both sides want plans for future relations to be set out by October along with a legally-binding treaty detailing the terms of the UK's withdrawal agreement.
Mr Barnier said the rest of the bloc had made clear it wants a partnership that is as close as possible but Britain's position on quitting the single market and customs union along with other policies meant it is "closing doors".
"The European Council has made clear that, if the UK's red lines were to evolve, the Union would be prepared to reconsider its offer," he said. "We are flexible, never dogmatic. We are open for business.
"But of course any change from the UK must respect our principles, the principles we have built with the UK over 45 years.
"In particular, the four freedoms of the single market go together. They are all indivisible.
"You cannot have free movement of services without free movement of goods, and so forth. And you cannot have free movement of goods without free movement of people."
Speaking on a local election campaign visit on Monday morning, Mrs May insisted that would not change course.
She said arrangements which are as "frictionless as possible" with the EU and the ability to strike trade deals around the world were both achievable under the proposals set out by the Government.
On a visit to a firm in the West Midlands, she told the BBC: "Coming out of the customs union means that we will be free to have those deals, deals that suit the UK.
"But I also recognise the importance to businesses like this of being able to have as frictionless a border as possible into the European Union."
Downing Street insisted the Government's position had not changed since Mrs May delivered her Mansion House speech in March.
Those plans included two options, either a "customs partnership" effectively collecting duties for Brussels for goods arriving in the UK but intended for EU markets or a "highly streamlined" arrangement making use of technology and regulatory co-operation.
But Mrs May is set to face calls from leading Brexiteers Boris Johnson, David Davis and Liam Fox to abandon her preferred form of customs deal, according to The Times.
A showdown is expected to come at a meeting of the Cabinet Brexit committee scheduled for Wednesday when the trio will tell the PM that the "customs partnership" would be unworkable, the report said.
The Prime Minister's official spokesman said: "We have put forward two options. They were set out in the Mansion House speech.
"Those are still the two options we are moving forward with."
He added: "We think both of the two options which we have put forward can provide solutions to the Irish border and to having a smooth customs arrangement with the EU."
Mrs May will be given an indication of the scale of the opposition she faces from pro-EU Tories over her customs union plan in a Commons debate on Thursday.
Though the looming Commons vote on a pro-customs union motion would be a symbolic, non-binding one, it has the potential to deepen Tory wounds on Brexit.
The Prime Minister's spokesman played down its significance, saying Thursday's event was a "routine backbench business debate".
But binding Commons votes on a customs union during debates on the Taxation (Cross-border Trade) Bill and European Union (Withdrawal) Bill will prove harder for Downing Street to dismiss.