European Commission president Jean-Claude 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".
And he insisted the EU was united over the issue of the Irish border, one of the main issues in the negotiation.
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".