In opening deals, London's benchmark FTSE 100 index of major blue-chip companies sank 0.7 percent to 7,132.56 points, compared with the closing level on Monday.
The stronger pound weighs on London-listed multinationals whose earnings abroad are converted back into sterling.
In the eurozone, Frankfurt's DAX 30 index dipped 0.5 percent at the open to 11,446.29 points and the Paris CAC 40 slid 0.4 percent to 5,212.86.
Asian indices also fell Tuesday as investors struggled to maintain momentum from the previous day's trade talks-fuelled surge.
Sterling rose further after a report that British Prime Minister Theresa May is considering putting off the March 29 deadline for Britain to leave the European Union if she is unable to push her own deal through parliament, in a bid to avert a painful no-deal divorce.
Adding upside to the currency was the announcement by opposition leader Jeremy Corbyn that his Labour Party would support a second referendum on leaving the bloc if its own plan for Brexit is not approved.