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London's benchmark FTSE 100 index of top companies added almost 0.6 percent to nearly 5,962 points compared with Tuesday's close.
In the eurozone, Frankfurt's DAX 30 gained 1.3 percent to 10,112.4 points and the Paris CAC 40 won 1.1 percent to stand at 4,426.8.
Most Asian equity markets also climbed, after more than a week of sharp losses fuelled by worries over China's economy, with sentiment buoyed by news that the country's exports had picked up in December.