Draft EU guidelines on the EU’s approach to the next phase of Brexit talks on future relations with the UK have been revealed.
They repeat EU warnings about “cherry-picking” and say leaving the customs union and single market “will have negative economic consequences”.
But it also suggests that the EU is ready to change its stance if the UK position “evolves”.
The document must be signed off by EU leaders before trade talks can start.
EU Council President Donald Tusk unveiled the documents at a press conference in Luxembourg.
The leaders of the remaining 27 EU states must then approve the plans at a Brussels summit on 22 March, setting the template for chief negotiator Michel Barnier for talks about the future UK-EU relationship.
The UK is due to leave the EU at the end of March 2019, and both sides say a deal on their future relationship needs to be agreed by this autumn to allow time for parliaments to approve the deal before Brexit happens.
The draft guidelines say there will be no UK membership of EU agencies or bodies after Brexit and existing fishing rights for EU vessels in UK waters will continue.
And the document says there must be limits on how deep a free trade agreement on services should be and it should include “ambitious” provisions on free movement of people.
The document says the “four freedoms” of the single market – the free flow of goods, services, money and people – are “indivisible” and “there can be no “cherry picking” through participation based on a sector-by-sector approach, that would undermine the integrity and proper functioning of the single market”.
But the European Council “confirms its readiness to initiate work towards a free trade agreement (FTA), to be finalised and concluded once the UK is no longer a member state”.
It adds: “Such an agreement cannot offer the same benefits as membership and cannot amount to participation in the single market or parts thereof.”
It comes as Chancellor Philip Hammond calls for financial services to be included in any future trade agreement.
The EU’s chief Brexit negotiator, Michel Barnier, has argued that such a deal had never been done before.
But Mr Hammond will say in a speech that the EU has in the past attempted similar agreements, such as in trade talks with the US and Canada.
“If it could be done with Canada or the USA… it could be done with the UK,” he will say.
“I am clear not only that it is possible to include financial services within a trade deal but that it is very much in our mutual interest to do so.”
The EU draft guidelines contain no mention of financial services.
The BBC’s Economics Editor Kamal Ahmed said the two sides appeared far apart but most people involved in the talks thought a deal was possible.
The European Parliament has stressed that its preferred option is for the UK to continue to be a member of the single market and customs union after Brexit, in a draft resolution, leaked to the Politico website.
The parliament does not have a formal role in the Brexit negotiations but does have a veto on the final deal.
The European Parliament document, which may be changed before it is adopted later on Wednesday, says non-EU members – even if very closely aligned to the bloc – cannot expect the same rights and benefits as EU members.
It also warns that the UK’s current “red lines” in Brexit talks “would lead to customs checks and verification which would affect global supply chains and manufacturing processes, even if tariff barriers can be avoided”.
It says a “deep and comprehensive” trade deal, of the kind envisioned by Theresa May, must entail “a binding interpretation role” for the European Court of Justice.
The European Parliament resolution also warns the UK against “cherry-picking of sectors of the internal market”.
BBC Brussels Correspondent Adam Fleming said the draft will look like a rejection of the speech Theresa May delivered on Friday setting out her vision of post-Brexit trade, but with some “wriggle room” and the possibility of much more if the UK softens some of its red lines.
European Parliament Brexit chief Guy Verhofstadt met UK ministers in Downing Street on Tuesday for talks on the rights of EU citizens in the EU, and vice versa, after Brexit.
The European Parliament is due to vote on the resolution, the fourth it has issued on Brexit, next week.
MPs in Westminster are, meanwhile, set to debate a Plaid Cymru call for UK nationals to be allowed to keep their EU citizenship after Brexit.
Plaid said EU citizenship would give holders the right to travel, live, study and work anywhere in the EU even after the UK leaves next year.
A UK government spokesman said only citizens of EU member states could hold EU citizenship.