The European Union's chief negotiator Michel Barnier on Monday said he hoped for a "constructive" start to Brexit talks with Britain as formal negotiations began in Brussels.

"I hope that today we can identify priorities and a timetable that would allow me to report to the (EU summit) later this week that we had a constructive opening of the negotiations," the Frenchman said as he greeted Britain's Brexit minister David Davis.

Davis said: "We are starting this negotiation in a positive and constructive tone determined to build a strong and special partnership with our allies in the European Union."