Jean Claude Juncker has said: "Slowly but surely, English is losing importance".
Speaking in English, the European Commission's chief Brexit negotiator, Michel Barnier, said a priority in the talks would be to guarantee rights for some 3.2 million EU citizens living in Britain and for some 1.2 million Britons living in EU member states.
"When we have a British government immediately after the United Kingdom election, we'll be very busy in engaging constructively in Article 50 negotiation for which we are ready", he added.
His dig at the United Kingdom came after European Council president Donald Tusk appealed for calm following an angry spat that saw Theresa May accuse some in the EU of seeking to influence the result of the UK's General Election.
However despite the call for calm, Juncker told the conference that Brexit is a "tragedy".
Criticised on the Brexit in recent days, British Prime Minister Theresa May counter-attacked on Wednesday accusing "European officials" of wanting to interfere in the British legislative elections and not wanting the success of the Brexit.
"In order to succeed we need discretion, moderation, mutual respect and a maximum of goodwill". The UK only joined in 1973, but over the years English became a main working language of EU institutions and officials in Brussels and Strasbourg and at the European Central Banks in Frankfurt.
Tusk's comments were a sobering warning of the risk of a breakdown in the negotiations, which could see Britain crash out without agreeing divorce terms or a transition to ease its exit from the EU's single market.More news: Paul Pogba to return for Manchester United vs Crystal Palace
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"This is not a helpful situation but, be that as it may, it's happened. the issues that concern the European Union, of which we are a member, will not change", he said after talks with Canadian Prime Minister Justin Trudeau.
"The European Commission has tightened its negotiating position".
With a wry smile, the former prime minister of Luxembourg said: "Despite the successes and despite the growth, our British friends have chose to leave the European Union, which is a tragedy".
European Council president Donald Tusk said: "These negotiations are hard enough as they are".
She said these were "deliberately timed to affect the result of the general election that will take place on June 8". If emotions get out of hand, they'll become impossible. We shouldn't underestimate the importance of the decision made by the British people.
Charles Grant, director of the Center for European Reform, said on Twitter that May had misunderstood Brussels' politicians' motives.
"The Conservatives are doing very well and that is nearly certainly likely to have some spillover into the local elections", he said.
Labour had 466 seats - a net loss of 137 - while the smaller, pro-EU Liberal Democrats, who had been hoping to pick up some momentum ahead of June's parliamentary election, had 167 seats, a net loss of 23.