"I've read papers that sometimes refer to some of us saying that the UK is the last possible partner with whom we want to negotiate trade. Forget this nonsense," Jyrki Katainen, one of six Commission vice presidents at the EU executive, told a news conference.
The EU has insisted that it will only begin negotiations about future economic relations with Britain once enough progress has been achieved on divorce matters, namely the rights of citizens, a payment by Britain to the EU and on the Northern Ireland border.
"As soon as we know when we can start negotiating about the future arrangement, (trade) negotiations will start then. There's no political priority that we want to keep the UK as the last in the queue," Katainen said.
The European Union in July struck a preliminary trade deal with Japan and is aiming to conclude talks with Mexico and the Mercosur countries - Argentina, Brazil, Paraguay and Uruguay - by the end of the year.
Further negotiations are underway with a range of countries and regions across the world and the bloc hopes to start and finish talks with Australia and New Zealand in the next two years.
Katainen, a former Finnish prime minister whose EU responsibilities are jobs, growth, investment and competitiveness, said the European Commission had shown it was capable of holding several trade negotiations at the same time.
"So no need to provoke the situation anymore. It is complicated enough," he said.
EU Trade chief Cecilia Malmstrom said the Commission, which negotiates trade deals on behalf of EU countries, had a "fantastic simultaneous capacity" to negotiation such accords.
"Keep calm. Don't panic," she said.
(Reporting by Philip Blenkinsop and Robin Emmott; Editing by Matthew Mpoke Bigg)