Seven train operators have suspended their services with a rare "do not travel" alert in force for railways in England and Wales.
The following rail organisations have cancelled services due to Storm Eunice: c2c, Chiltern Railways, Great Western Railway, Greater Anglia, South Western Railway, Southeastern and Transport for Wales.
Network Rail closed all routes in Kent while every line in south-east London was blocked by trees.
South Western Railway said record-breaking winds had caused 'multiple incidents' - already downing 30 trees across routes.
In a joint statement with Network Rail, the operator said: "As a result, all SWR services have been suspended and we strongly urge customers not to travel toady.
"While we are working hard to try to restore some services later tonight, we cannot guarantee any trains will run for the rest of the day and customers should make alternative travel arrangements if possible."
Network Rail tweeted a dramatic clip of the roof of a building blowing onto the tracks at Banbury, adding that it was another example of why services have been cancelled across the country.
Jacqueline Starr, chief executive at industry body the Rail Delivery Group, said: "Storm Eunice is causing widespread damage and we've had to respond by closing lines to keep our customers and staff safe.
"We're telling people not to travel today and instead to claim a fee-free refund or use their ticket over the weekend."
The Port of Dover announced it was closed "in the interests of customer and staff safety", meaning no ferries could operate between Dover and Calais.
Several sailings across the Irish Sea were also cancelled.
National Highway, which operates the Severn bridges, said its staff were "being abused" for taking action to "keep road users safe".
Traffic Wales, the Welsh Government's traffic information service for motorways and trunk roads, warned that "many HGVs are ignoring the safety advice on Britannia Bridge".
The bridge, which connects the island of Anglesey with mainland Wales, is closed to all traffic except cars and car-derived vans.
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There were one-hour delays on the M25 due to the closure of the Queen Elizabeth II bridge, which is part of the Dartford Crossing.
The RAC said the number of call-outs to broken-down vehicles was lower than normal, indicating that many people were "taking the weather warnings seriously and not setting out".
It added: "The fact many roads are so clear is a sign that today is not a safe day to be driving."
Transport for London urged people to avoid non-essential journeys in the capital.
As of Friday afternoon there were severe delays on to the tube's District Line, Jubilee Line and Piccadilly line, while TfL Rail was suspended.
Others were part suspended.
A TfL spokesperson said: "We are doing all we can to ensure we are prepared for any impact with extra staff ready to respond quickly to any incidents but some services will be affected by the extreme weather. "We are also urging Londoners to please take care if they travel around the city."
