The benchmark FTSE 100 index lost 0.3 percent to 7,131.23 points compared with the close on Tuesday.
In the eurozone, Frankfurt's DAX 30 index dropped 0.2 percent to 11,499.32 points and the Paris CAC 40 slipped 0.1 percent to 5,263.01.
British MPs will Wednesday vote on whether the UK should leave the European Union without a deal in just over two weeks, after overwhelmingly rejecting the country's draft Brexit divorce agreement with Brussels.
The House of Commons is expected to vote against a 'no deal' Brexit, although this could still happen on March 29 unless the British parliament can agree on what should happen instead.
MPs on Tuesday rejected for a second time the withdrawal deal negotiated by Prime Minister Theresa May, despite her obtaining last-minute assurances from EU officials.
Meanwhile ahead of Wednesday 'no deal' vote, finance minister Philip Hammond updates the government's spending and tax plans that depend heavily on the nature of Brexit.
Contained within The Spring Statement, an update on the main annual budget announcement last October, will be the government's latest forecasts for UK growth -- widely expected to be downgraded owing to Brexit uncertainty and global economic headwinds.