"Clearly this has been a difficult night for many Londoners, and continues to be an incredibly trying morning," said Mayor of London Boris Johnson.
He said transport and emergency services were "working flat out in an effort to keep London moving and minimise disruption as far as is possible" and said he would be chairing a meeting with all the relevant agency chiefs.
Several major bridges were also closed, including the Severn Bridge over the estuary between England and Wales.
The Met Office said 50 millimetres (almost two inches) of rain fell in some areas overnight as the storm tracked eastwards across Britain.
The Environment Agency issued 133 flood alerts and warned that flooding was likely across 12 areas of southwest England including Devon and Cornwall.
The storm, named St Jude in Britain after the patron saint of lost causes whose feast day is Monday, had earlier been predicted to be the worst for a decade.
Forecaster Helen Chivers had told AFP the expected damage was likely to be comparable with a storm seen in October 2002, although stronger winds have been recorded since then.
However, the devastation fell far short of that caused by the "Great Storm" of October 1987, which left 18 people dead in Britain and four in France and caused damage worth 1 billion ($1.6 billion or 1.2 billion euros at current exchange rates).
The Met Office had given plenty of warning of St Jude - in contrast to 1987 when BBC weatherman Michael Fish famously assured viewers just hours beforehand that no hurricane winds were expected.