Britain cannot be a member of the European single market and regain full control over immigration from the continent, Jean-Claude Juncker has suggested.
The European Commission president said the UK cannot expect "a la carte" access to the free trade zone once Brexit is delivered.
European leaders see the free movement of EU citizens as a condition for membership of the single market.
The issue has become central to the Brexit debate and has caused friction within the Government.
Prime Minister Theresa May has slapped down Brexit Secretary David Davis for saying it was "very improbable" that the UK could be in the single market and also control its borders.
At his state of the European Union address to the European Parliament, Mr Juncker warned Britain: "There can be no a la carte access to the single market."
He also called on the Government to trigger Article 50 - the formal process for leaving the EU - as soon as possible.
"We would be happy if the request for Brexit could happen as quickly as possible so that we could take the specific steps which need to happen," he said.