The EU's chief Brexit negotiator, Michel Barnier, said London should be "under no illusion" on financial services as there would be "no general, global, permanent equivalence" with Britain.
He told Julia Hartley-Brewer that Brits need to "rediscover" their optimism.
It is believed that the new system will be closer to U.S. regulations than to those of the EU. During the transition period, the British government and European Union leaders will try to negotiate a free trade deal and agreements covering other areas like security cooperation.
European Commission president Ursula von der Leyen said she was "surprised" by the proposition, pointing out that Australia is now in talks with the EU to improve its current agreement with the bloc. "But of course this requires corresponding guarantees on fair competiton and social, environmental and consumer standards".
She added however that "I personally believe that we should be way more ambitious" and reiterated Europe's conditions Britain would have to abide by if an accord were to be struck. "But all these models, whatever you choose, have one thing in common - they all come not only with rights but also with obligations for both sides".
The commission said the United Kingdom has two months to notify it of changes to the way the tax works or face the prospect of being taken to European Union courts.
Britain wants the trade agreement to cover goods and services and exclude nearly all tariffs.
The UK Treasury had included the demand for so-called permanent equivalence in a draft of its opening positions for next month's trade negotiations with the European Union - some of which were revealed in a document that was photographed as Chancellor of the Exchequer Sajid Javid carried it in Downing Street on Monday. "We will keep control of these tools, and we will retain the free hand to take our own decisions".
"We will no longer be rule-takers, but we remain committed to the highest worldwide standards of financial regulation and to shaping global rule-making".
His words came shortly after it emerged the United Kingdom would be seeking a "permanent equivalence" regime for financial services that would last for "decades to come".
The British Retail Consortium said the government would have to move fast to get infrastructure in place for 2021, warning that without adequate preparations the availability of goods on shelves would be disrupted, with fresh fruit and vegetables especially vulnerable.
"Come what may, on January 1 we will be imposing checks on all products entering the single market, just as we do to every other third country in the world", he said.
With the EU having already presented its negotiating stance earlier in February, Barnier and EU Commission President Ursula von der Leyen addressed MEPs during Tuesday's Strasbourg plenary session as the European Parliament debated a resolution on its stance on the EU-UK Partnership which will be put to a vote on Wednesday.