London's benchmark FTSE 100 index of major blue-chip companies climbed 0.3 percent to 7,435.76 points.
In the eurozone, Frankfurt's DAX 30 index also rose 0.3 percent to 13,243.48 points and the Paris CAC 40 added 0.4 percent to 5,885.81.
However, Asian stock markets tumbled again on Tuesday as the toll from a rapidly spreading Chinese virus spiked to more than 100 dead and thousands infected, with investors fretting over the impact on an already fragile world economy.
"European markets have set aside some of the concerns in relation to coronavirus. Basically, speculators are back in town and ready to support the markets," said Ava Trade analyst Naeem Aslam.
"For them, the current sell-off is an opportunity. Having said this, the theme is not the same across global markets as they are still under the influence of this virus."
In a fierce global selloff on Monday, London tanked 2.3 percent while Frankfurt and Paris each slumped by 2.7 percent.