In initial deals, London's benchmark FTSE 100 index declined 0.3 percent to 6,297.4 points compared with Tuesday's closing level.
In the eurozone, the Paris CAC 40 dipped 0.2 percent to 4,690.3 points. Frankfurt's DAX 30 fell 0.05 percent to 10,855.2 points ahead of an early finish at 1300 GMT.
Both Paris and London will have shortened trading hours on Thursday, while Frankfurt will remain closed.
All three main European markets will be shut on New Year's Day on Friday, and will re-open for business on Monday January 4.
Most major Asia-Pacific stock markets also turned lower Wednesday as another retreat in oil prices dented buying sentiment, but Tokyo ended on a high note as one of the best-performers of 2015.