The British and French stock markets rose at the open on Monday for the final trading day of 2018, but Frankfurt remains shut for the festive break.
In initial deals, London's benchmark FTSE 100 index of major British blue-chip companies climbed 0.2% to 6 746.69 points.
In the eurozone, the Paris CAC 40 gained 0.6% to 4 708.74 points, compared with Friday's closing level.
London and Paris face half-day New Year's Eve
Frankfurt meanwhile remains closed for business after the DAX 30 index gained 1.7% on Friday to finish at 10 558.96 points.
However, the DAX index dived 18.3% in value over the course of 2018, in a tumultuous and volatile year for stock markets worldwide.