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London's benchmark FTSE 100 index gained 0.2 percent to 7,065.11 points, with investors keenly awaiting an announcement that Britain has sealed a deal over Brexit.
In the eurozone, Frankfurt's DAX 30 jumped 0.7 percent to 11,402.52 points and the Paris CAC 40 rose 0.4 percent to 5,077.57.
Global stock markets had tumbled Monday, with Frankfurt shedding 1.8 percent, in part on concerns over Tuesday's EU-deadline for Rome to revise its 2019 budget.