The European Union will not give in to British demands for full access to the bloc's single market unless London allows free movement of people, Ireland's prime minister Enda Kenny said today.

Britain's minister charged with negotiating Brexit, David Davis, said last week that it was pressing for a "unique" deal with the EU to restore sovereignty, reduce immigration by controlling its borders and boost trade with the bloc after the split.

Enda Kenny has made Ireland's position clear. Photo: Shutterstock

But European leaders have warned Britain it cannot cherry pick which rules it follows if it wants to continue to have unfettered access to Europe's markets.

"Let me tell you that around the European Council table, that is an issue that will not be given in on," Kenny said in an interview with Ireland's Newstalk radio station.

He said the issue had been "very directly addressed" by European leaders to the British government.

Kenny said the British government did not appear to have a clear position on what form of Brexit it was trying to achieve.

"They don't have a definite horizon as to where they want to be," he said.