Britain's decision to leave the EU is irreversible, German Chancellor Angela Merkel says following summit talks in Brussels with British Prime Minister David Cameron and the bloc's other leaders.

"This is not the hour for wishful thinking the referendum stands as a reality," she said.

"The atmosphere was serious, amicable and borne by the awareness that this is more of a sad event, but that it is a reality," Merkel said of the leaders' talks, noting that consequences now need to be drawn.