The pan-European STOXX 600 traded down 2.9 percent early on Monday. The internationally focused FTSE 100 traded 1.7 percent lower and the FTSE 250 — which tracks the next 250 biggest U.K. companies — declined by 5.2 percent.
The U.K. government is yet to indicate how negotiations to leave the EU trading bloc will proceed. Meanwhile, Prime Minister David Cameron has said he would resign by October and the leader of the opposing Labour Party faces a "vote of no confidence" on Monday.
"Day four after the seismic referendum result and the only thing that's crystal clear is that the U.K. is in the midst of one hell of a political crisis," Chris Scicluna, head of economic research at Daiwa Capital Markets, said in a note on Monday.
Major Asian indexes closed higher on Monday, with Japan's Nikkei leading gains, ending up 2.4 percent. This followed media reports that Tokyo would step in, if necessary, to stabilize the yen, which has gained from the safe-haven bid that followed the Brexit vote.