The UK will come to regret its decision to leave the European Union, Jean-Claude Juncker has suggested.
European Commission president Mr Juncker said things "cannot remain as they are" for the UK in its relationship with the EU after leaving the bloc.
Addressing the European Parliament, Mr Juncker was cheered by Eurosceptic MEPs as he noted the UK's departure was due on March 29 2019.
Responding to their applause, Mr Juncker said the time would come "when you will regret your decision".
But former Ukip leader Nigel Farage claimed the European Commission was seeking to "bully" the UK and suggested Theresa May should back a departure from the bloc without a transition deal.
In a message to Mrs May ahead of next week's European Council summit, Mr Juncker said the EU needed "more clarity on how the UK sees its future relationship".
Mr Juncker said "cherry-picking is not going to be possible" in the future trade relationship between the UK and EU.
"I would rather have preferred Britain not to have decided to leave the European Union, but anyone who leaves the European Union has to know, frankly, what this means," he said.
"If you decide to jettison, leave behind, the common agreements and rules, then you have to accept that things cannot remain as they are."
Mr Juncker said the controversial "backstop" proposal for dealing with the border between Northern Ireland and the Republic "translates faithfully" the agreement reached between Mrs May and the EU in December.
He said the EU was ready to work with the UK on its preferred option of the border issue being resolved in the future trade deal, or by other specific measures.
But he added "we need to receive concrete proposals from the UK first".
Mr Juncker said: "The 27 member states stand firm and united when it comes to Ireland. For us this is not an Irish issue, it is a European issue."
But he was heckled by one MEP who shouted "it is a British issue".
Brussels' chief Brexit negotiator Michel Barnier said Mrs May's decision to leave the single market and customs union was "closing doors" to possible models of future co-operation.
Mr Barnier added that it was a "rather surprising idea" to think the EU could accept convergence in some areas "and at the same time open up the possibility for divergence when there is a comparative advantage to be had" for the UK.
"It's time to face up to the hard facts," he said.
"The UK is choosing to leave the union, the single market and the customs union, we have noted that.
"Do they also want to distance themselves from our regulatory model, the one that we have constructed together with you - and you with us - for 44 years?"
He questioned whether that could result in the UK "dumping" products on EU markets by diverging from the bloc's economic and social model after Brexit.
The European Parliament's Brexit co-ordinator Guy Verhofstadt also called for more details from the Prime Minister.
He said: "There was this Mansion House speech by Mrs May, but it was mainly repeating the red lines that we know already."
Mr Verhofstadt said it was time to move beyond "slogans" and "soundbites".
His European Parliament motion calls for an "association agreement" to deal with the future UK-EU relationship.
But it insists on a "binding interpretation role" for the European Court of Justice (CJEU) and rejects UK efforts to "cherry-pick" single market access for particular sectors, such as the financial services industry.
Mr Farage, a supporter of US President Donald Trump, said the UK should leave the EU without a transition deal and claimed a transatlantic trade deal could be struck "in 48 hours".
He said: "Mrs May, we did not vote for a transition period, we voted to leave this organisation, we voted to leave the customs union, we voted to leave the single market.
"Please Mrs May, at this summit next week, do what Trump has done - stand strong against the European Commission, against the unelected bullies."