The UK will come to "regret" the decision to leave the EU, European Commission president Jean-Claude Juncker has warned.
Addressing the European Parliament, Mr Juncker was cheered by Eurosceptic MEPs as he noted the UK's departure was due on 29 March, 2019.
In response he said the time would come "when you will regret your decision".
MEPs' Brexit representative, Guy Verhofstadt, said the UK had to move beyond the "slogans and soundbites".
But he said that the UK and EU were "very near" to an agreement on citizens' rights post Brexit.
Mr Juncker told MEPs in Strasbourg there was an "increasing urgency" to negotiate the UK's orderly withdrawal from the EU.
He did not want EU citizens to "fall victim to Brexit", he said, adding that it was important to secure their rights.
Mr Juncker repeated the EU side's line that "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."
He urged Theresa May to give "more clarity on how the UK sees its future relationship with the EU".
He called for further British proposals on how to avoid a hard border in Northern Ireland, which he calls a "European issue" not just an "Irish issue".
But he was heckled by UKIP's David Coburn, who shouted: "It is a British issue."
Meanwhile, former UKIP leader Nigel Farage argued that Mrs May should channel US President Donald Trump when she meets EU leaders next week.
Referring to the dispute with the US over steel and aluminium tariffs, he said the UK could sign its own trade deal with the US "in 48 hours" if it was not a member of the EU.
He urged Mrs May to abandon plans for a transition period post Brexit, saying the UK voted "to leave this organisation", the customs union and single market.
"So please Mrs May at this summit next week, do what Trump has done, stand strong against the European Commission, against the unelected bullies," he said.
Interim UKIP leader Gerard Batten added that the European Commission "wants unconditional surrender" from the UK negotiators.
He said Mrs May would settle for "conditional surrender", but added that "UKIP's position is no surrender" and his party would not accept "subservience" to the EU in the future relationship.
Liberal Democrat MEP Catherine Bearder argued that the UK government had "no plan for Northern Ireland, no plan for its citizens and no plans for its businesses", adding that "no clear plan is a dereliction of its duty".
"Whatever the deal might be, we as Liberal Democrats demand the people have a say on it," she told MEPs. "Or, as my hashtag says 'give us a say Mrs May'."
Conservative MEP David Campbell Bannerman urged European colleagues not to be so negative about Brexit.
He said the UK will become "the largest single market of the EU when we leave, bigger than China, US, Japan, for example".
"We have a £75m deficit with the EU of your goods and we employ 1.5m Germans through cars, etc - and the City of London is very important to funding EU businesses. I've heard none of this today," he added.