"We will have two separate markets instead of one single market," Barnier told a press conference, Xinhua news agency reported.
He said that customs rules will apply between the two sides, and access to the new market could be subject to certification, market authorisation and supervision.
"This means, for example, that UK financial services suppliers will no longer have the passporting rights," he elaborated.
"Passporting rights" refer to the rights that allow companies and financial services firms to operate in any EU or European Economic Area (EEA) country without being subject to further authorization from each country.
Trade in goods and services will be subject to regulatory checks as all imports of goods or services supplied in the EU will have to comply with the EU rules, he said.
As the UK chose to leave the EU on January 31, 2020, the country has left the single market and the customs union as well.
The remaining 27 EU member states have agreed to negotiate a trade deal with the UK by the end of 2020.
While European Commission President Ursula von der Leyen has said it was impossible to iron out all the details within that timeframe, UK law forbids the extension of the transition period.
On Monday, Barnier proposed comprehensive negotiating directives, covering areas such as trade, judicial cooperation, foreign policy, security and defence.
The directives are to be formally presented to the Council of the EU, which will authorize the European Commission to open negotiations.
"It's now time to get down to work. Time is short. We will negotiate in a fair and transparent manner, but we will defend EU interests, and the interests of our citizens, right until the end," von der Leyen said.
( With inputs from IANS )