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London's benchmark FTSE 100 index of major blue-chip companies was down 0.6 percent at 7,012.77 points.
In the eurozone, Frankfurt's DAX 30 lost nearly 0.7 percent to 11,394.75 points and the Paris CAC 40 shed almost 0.8 percent to 5,062.44.
British Prime Minister Theresa May will seek her cabinet's approval later Wednesday for a long-awaited divorce deal with the EU, but hardline Brexiteer MPs warned they will seek to block it in parliament.
After months of talks, May announced late Tuesday that negotiators had finally reached a deal on the terms of Britain's withdrawal from the EU next March.
"We are now at the crunch point for Brexit," said Markets.com analyst Neil Wilson.