Speaking at a news conference after two full days of talks in Brussels, Michel Barnier said he was "disappointed and concerned" because British Prime Minister Boris Johnson had told the EU he wanted to speed up the negotiating process over the summer.
The former French foreign minister said British negotiators had "not shown any real willingness to move forward on issues of fundamental importance for the European Union."
Barnier said a deal with "zero tariff and zero quota" would require the EU and its former member to reach a deal on a "credible and operational framework of level-playing field," as well as on fisheries.
He added talks with Britain this week often appeared to going backwards rather than forwards and, at this point, it looked unlikely that a deal could be clinched before the year-end deadline.
Britain became the first country ever to leave the EU on January 31. The two are now negotiating a new partnership, to be effective from 2021, on everything from trade and transport to energy and security.