Train companies have cancelled early-morning services, and flights into London have been reduced.
Gusts of up to 80mph (130km/h) are predicted as the weather hits the South West then moves north and eastwards and there are fears of flooding and damage.
The prime minister has chaired talks about plans to protect the public.
Meanwhile the search for a missing 14-year-old boy who was swept away by the sea in East Sussex has been suspended.
|Waves in Newquay Cornwall|
Travel warnings included:
South West Trains have advised people not to travel on Monday with most services not running until at least 08:00 GMT to allow Network Rail to check lines. A reduced timetable will be in operation, with some trains limited to speeds of 50mph
East Coast will operate a revised emergency timetable on Monday, with trains stopping at Peterborough until 10:00 GMT, and limited to speeds of 50mph afterwards
First Great Western and Virgin West Coast main line are also running an amended service until 10:00 GMT and 09:00 GMT respectively
First Capital Connect and C2C said services are unlikely to begin until 09:00 GMT. Greater Anglia, Southern and Gatwick Express have said services on Monday will not run until it is declared safe to do so
London Overground will not run a service on Monday before 09:00 GMT, while First Great Western has warned of extended travelling times and Southeastern said it is likely to start running services late
Airports including Heathrow and Gatwick are warning of possible disruption to flights, advising passengers to check with airlines
Airlines operating in and out of Heathrow have been instructed to reduce their schedules by between 5% and 20% between the hours of 06:00 GMT and 22:30 GMT, leading to about 60 flight cancellations. It is not yet clear how many of those will be short-haul or long-haul flights
EasyJet has warned passengers there could be disruption to flights on Monday. It said no trains would run to Gatwick, Southend, Stansted or Luton airports before 09:00 GMT
Eurostar said it will not be running trains on Monday until 07:00 GMT, with early services from London and Brussels subject to delays. It expects to run a full service after 07:00 GMT and passengers are advised to arrive at the scheduled time
Several ferry companies have also cancelled services, including some English Channel and Irish Sea crossings
Several bridges including the M48 Severn Crossing, the A249 Sheppey Crossing in Kent, and the Tamar Bridge which joins Cornwall and Devon are closed. There also are plans to shut the M4 Severn bridge and the Queen Elizabeth II bridge on the M25 on Monday morning, with traffic directed through the tunnel part of the crossing
The Highways Agency is advising motorists to check the weather forecast and road conditions before they travel
|Stranded Passengers at Kings Cross Station|
Four people have died after a storm battered southern Britain, leading to 625,000 homes losing power, and major rush-hour disruption to commuters.
A teenager in Kent and a man in Watford were killed by falling trees.
A man and a woman died in west London after a falling tree caused a suspected gas explosion and a house to collapse.
Many rail companies suspended morning services before running reduced services later. They say operations will be back to normal on Tuesday.
Flights and ferry crossing were also affected as the storm moved across Britain.
BBC forecasters say the storm, which began on Sunday night and saw heavy rain fall across many areas and wind speeds of more than 70mph, moved out of the UK shortly after 12:00 GMT - leaving a "broadly windy day" behind.
|Needles Old Battery - Isle of Wight|
The strongest gust of 99mph (159km/h) during the storm was recorded at Needles Old Battery, Isle of Wight, at 05:00 GMT.
|Mobile Home Crushed by tree - killing teen|
Bethany Freeman, 17, suffered fatal injuries when the tree came down on the caravan where she was sleeping in Hever, near Edenbridge, at about 07:20 GMT.
The caravan was next to the house she lived in with her family and she had been sleeping there while renovations were carried out.
Donal Drohan, 51, from Harrow, was pronounced dead at the scene after a tree crushed a red Peugeot 307 at Lower High Street in Watford, Hertfordshire, at 6:50 GMT.
Mark Joseph, who was passing by before the emergency services arrived, said: "We tried to assist, trying to get the tree off, but it was impossible... The poor chap didn't stand a chance."
The man and women who died in west London were found after three houses collapsed and two others were damaged following a gas explosion after a tree fell during high winds in Hounslow, the London Fire Brigade said. Three people injured in the incident were taken to hospital.
The search for the 14-year-old boy - who has been named as Dylan Alkins - who was swept away in Newhaven, East Sussex on Sunday has resumed
|Bus overturned in Suffolk|
A double-decker bus rolled over in Suffolk, injuring the driver and several passengers. Witnesses told police the vehicle blew over at 08:00 GMT, rolling onto its side and coming to a stop in a field in Hadleigh
Both reactors in Dungeness power station's B units were automatically shut down after power to the site was cut off. The site's own generators are providing power to the site.
The Metropolitan Police says it received 792 calls to its 101 and 999 numbers between 06:00 and 08:00 GMT, compared with the 200 it would normally expect. The most common call was for "tree in road"
|Southwest Tracks in Alton Hampshire|
Police say 125 trees fallen across Sussex including one on a taxi in Eastbourne, from which the driver climbed out uninjured.
The helter-skelter at Clacton Pier in Essex has blown down.
London Mayor Boris Johnson has chaired an emergency resilience meeting involving all emergency services and relevant agencies - and later made a statement thanking them for their work.
|Collapsed crane on the roof of the Cabinet Office|
Deputy Prime Minister Nick Clegg cancelled his monthly press conference after a crane collapsed on the roof of the Cabinet Office
|Storm as of 00:00 Monday 10/28|
We had some gusty winds in our area, but our trees are all fairly small in this area and protected by taller buildings. Throughout the night it sounded like shutters were beating against the windows. The streets were wet, but it was no longer raining by 10:00 AM.