Mr Juncker’s comments represent a further setback to hopes that the UK might be able to maintain tariff-free trade with its former partners while imposing controls on immigration from the EU.
They follow French President Francois Hollande’s warning, after talks with Theresa May last week, that Britain faced a choice - “to remain in the Single Market and then assume the free movement that goes with it or to have another status”.
Free movement of labour between EU states is regarded by Brussels as one of the fundamental principles underpinning the 28-nation bloc, and many member-states are expected to resist making an exception for the UK.
Speaking to French TV channel France 2, Mr Juncker denied he was taking a “hard line” on the UK.
“It’s not a hard line, it’s common sense,” he told the Telematin programme. “It reflects the philosophy of the European project itself.
“The day after the Brexit vote, I said - along with president (Donald) Tusk of the European Council and president (Martin) Schulz of the European Parliament that this was the position of the EU. No access to the internal market if you do not accept the rules - without exception or nuance - that make up the internal market system.”
Mr Juncker said he would have preferred talks on Brexit to begin as soon as possible, but acknowledged that the UK Government will need “several months to fine-tune its position”.
The two-year process of negotiating the UK’s withdrawal will not begin until London informs the European Council of its intention to leave under Article 50 of the Lisbon Treaty.
Mr Juncker said: “I do not have a deadline, because Article 50 of the Treaty, which marks out the route to the exit, can only be activated by the UK. The Commission and the other member states can’t activate it.
“I would have liked the UK to present us with its resignation letter as soon as possible, because I would have expected that the British, especially those who wanted to leave the EU, would have prepared themselves for this possibility.
“Well, that wasn’t the case. The British Government needs several months to fine tune its position. Our British friends know that there will be no negotiation before notification of their farewell letter.”
The Commission president said he was looking forward to meeting Foreign Secretary Boris Johnson, who before the June 23 referendum drew a comparison between the EU’s efforts to unify Europe and those of Adolf Hitler.
“He may notice then that the difference between Hitler and me is more than a matter of nuance,” said Mr Juncker.