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Britain's Prime Minister Theresa May has called on her fellow European Union member countries' leaders to apply some level of urgency in rounding off this stage of Brexit talks so that both parties can commence future trade discussions.

EU leaders have rebuffed May's calls by saying they need far more details than Britain is currently providing.

Prime Minister May made her appeal during the European Summit in Brussels where the other 27 EU leaders were scheduled to decide on whether the current state of Brexit talks were advanced enough to trigger discussions on Britain's future trading arrangements with the Union.

"I particularly want to see an urgency in reaching an agreement on citizens' rights," May said on the sidelines of the summit.

"I set out a few weeks ago in Florence a very bold and ambitious agenda and vision for our future partnership between the EU and the UK ... I look forward to us being able to progress that in the weeks ahead," added May, referring to a speech she gave in the Italian city last month, where she proposed a two-year transition after Brexit.

However, several other EU leaders noted that there had not been sufficient progress and called for more details from the British side.

"What they [Britain] always say is that they want to continue to have the closest possible relationship with Europe and with Ireland," said Irish Prime Minister Leo Varadkar.

"We already have the closest possible relationship: it's called the European Union. And I think we need a little bit more detail - a lot more detail, in fact - on how you can square the idea of the closest possible relationship with the circle of the fact that they are departing from that."