The prickly EU official made it clear that he would not deal with any information about a security pact between the EU and Britain at the annual Munich Security Conference today.
Mr Juncker blasted: “We need a security alliance between the UK and the EU, but we can’t mix that question up with other questions relating to Brexit.”
“I wouldn’t like to put security policy considerations with trade policy considerations in one hat. I understand why some would like to do that, but we don’t want to.”
Prime Minister Theresa May fired back that it was also important for EU bosses to sign a new security treaty with Britain.
She said that it was important not to let ideological differences block co-operation in that sector after Brexit.
Mrs May said key aspects of a future partnership should be effective from 2019, emphasising she was unconditionally committed to European security. Britain is due to leave the European Union in March of next year.
Speaking at the Security Conference, she said Britain would respect the role of the European Court of Justice (ECJ) with regard to certain security agencies, but would not be subject to its jurisdiction.
She said: “We must do whatever is most practical and pragmatic in ensuring our collective security.”
“This cannot be a time when any of us allow competition between partners, rigid institutional restrictions or deep-seated ideology to inhibit our co-operation and jeopardise the security of our citizens.”
Mrs May argued that leaving the ECJ’s jurisdiction should not make it harder to extradite terrorism suspects or share information.
Britain said that the issue of security is too important to become entangled in the minutiae of Brexit negotiations, something that Mr Juncker agreed with.
The interior minister last year told the EU it could “take our information with us” if it left the bloc without a deal on security, jeopardising its membership of agencies such as Europol.
A government’s policy paper on security acknowledged a new form of agreement was needed because there was no clear precedent for security co-operation between the EU and other states.
Mrs May said: “I recognise there is no existing security agreement between the EU and a third country that captures the full depth and breadth of our existing relationship,” said, though there were precedents for strategic relationships between the EU and other countries in other areas.
“There is no legal or operational reason why such an agreement could not be reached in the area of internal security.”