The message comes just ahead of a meeting between UK Prime Minister Theresa May and EU leaders at a specially convened summit in Brussels on Wednesday.
It is expected that May will ask for a short delay to Brexit at the emergency summit, probably until the end of June, although this is not favoured by many EU leaders, including European Council President Donald Tusk, who are thought to be pressing for a longer, “flexible”, delay until the end of this year.
Earlier on Wednesday, the Commission issued a statement on the possible ‘no-deal' scenario if the UK - as still could happen - leaves the EU this Friday "or at a later date."
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It says it has taken stock of the European Union’s “intense” ‘no-deal’ preparations and has issued practical guidance to Member States in 5 areas: citizens’ residence and social security entitlements, data protection, medicine and medical devices, police and judicial cooperation in criminal matters and fisheries.
The statement says that in the event of a no deal "the UK will become a third country without any transitional arrangements."
All EU primary and secondary law will cease to apply to the UK from that moment onwards and there will be no transition period, as provided for in the Withdrawal Agreement.
The Commission said, "This will obviously cause significant disruption for citizens and businesses."
"UK citizens will no longer be citizens of the European Union. They will be subject to additional checks when crossing borders into the EU. Again, Member States have made considerable preparations at ports and airports to ensure that these checks are done as efficiently as possible, but they may nevertheless cause delays" European Commission
In such a scenario, the UK's relations with the EU would be governed by public international law, including World Trade Organisation rules.
The EU, warns the executive, will be required to immediately apply its rules and tariffs at its borders with the UK, including checks and controls for customs, sanitary and phytosanitary standards and "verification of compliance with EU norms."
"Despite the considerable preparations of the Member States' customs authorities," it says, "these controls could cause significant delays at the borders."
UK entities would also cease to be eligible to receive EU grants and to participate in EU procurement procedures under current terms.
"UK citizens will no longer be citizens of the European Union. They will be subject to additional checks when crossing borders into the EU. Again, Member States have made considerable preparations at ports and airports to ensure that these checks are done as efficiently as possible, but they may nevertheless cause delays."
The Commission also says that while the impact of a ‘no-deal' scenario will be felt throughout the EU, "it is clear" that some regions and economic sectors will be affected more directly.
The Commission has explored how current EU funds and programmes could be mobilised in case of a ‘no-deal' and in the case the UK fails to pay what is envisaged under the contingency EU budget regulation.
Meanwhile, Parliament's political group leaders and the Brexit steering group have issued a statement, saying, "when Prime Minister May comes to the European Council today she cannot come empty handed."
"We expect the Prime Minister to indicate what are the prospects of the cross-party talks between the Government and the Labour Party and their anticipated results and whether a solid parliamentary majority in support of such an agreement exists."
"If not, she should indicate clearly the way forward, be it a referendum, a general election, or a revocation. In this context, the European Council would be advised to provide the UK with an extension which should be appropriately framed to respect the principle of sincere cooperation and under no circumstance allow the Withdrawal Agreement to be reopened or negotiations on the future relations initiated."