The European Commission said it would "take some time" for the bloc to agree its position.
The prospect of trade talks not commencing until March could add to pressure for an extension to the negotiating period, but Prime Minister Boris Johnson has repeatedly insisted that a deal must be reached by the end of December.
European Commission spokesman Eric Mamer said the process of agreeing the EU's position could only begin after Brexit.
"This, we know, will take some time, which is why we have said we will start negotiations as quickly as we can, but it will certainly not be before the end of February, beginning of March," he said.
"This is not a slowing down or speeding up of the process.
"This is simply the nature of the institutional process and the consultations that need to take place before the negotiation directives can be formally adopted."
The delay leaves open the option of the UK beginning trade talks with the US before negotiations begin with Brussels.
Officials would not be drawn on a timetable for UK-US negotiations, but the two sides have made "extensive preparations".
Donald Trump has repeatedly spoken of his desire to reach an agreement with Mr Johnson, and the timing of the US presidential election means that a deal in the summer of 2020 could be his goal.
The Prime Minister's official spokesman said: "We are free to begin discussions with countries around the world from February 1. We are ready to begin discussions with the EU from February 1.
"The EU have various processes to go through before they are ready to sit down and have those discussions with us."
The UK remains committed to agreeing a deal with Brussels by the end of the year.
"The EU have agreed formally to complete this process by December 2020, that is what we would expect to be achieved," the spokesman said.
The EU repeated its warning that the UK's plans to diverge from the Brussels rulebook would limit access to the bloc's markets.
Mr Mamer said: "There is a link between moving away from EU regulations and the degree of access that is possible into the single market."
The Prime Minister's spokesman said the new situation would mean "it will be the UK which determines its own rules and laws".
"It will not be a ruletaker from Brussels or the EU's institutions."