A spokesperson for Scotland Yard confirmed the body of a man was found in the rubble at around 2pm, with a woman's body being found shortly after.
At least another two people were killed in the storm which forced a nuclear power plant to close and left hundreds of thousands of homes without electricity.
Hurricane-force winds, which hit overnight, caused huge travel disruption as train companies cancelled hundreds of services due to the risk of falling trees and debris.
The extreme weather conditions have now cleared the UK, meteorologists say, but leave a trail of destruction across the south of England and Wales.
Tens of thousands of commuters face difficult journeys home as the rail network is still blighted by problems caused by hurricane force winds.
The girl, named locally as Bethany Freeman, was crushed to death.
A 17-year-old girl was killed in Hever, Kent, when 80 mph winds blew a tree on to the caravan she was sleeping in at 7.18am.
Neighbours used chainsaws to try and rescue the 17-year-old after the caravan where she was sleeping was crushed by a 40-ft fir tree.
The girl, named locally as Bethany Freeman, was crushed to death. A second nearby caravan, where Bethany's mum Tessa Pierce was believed to be staying, was left untouched.
Police said that a man in his 50s died after a tree fell on his car in Watford and a 14-year-old boy is still missing after being swept out to sea in Newhaven, Sussex, on Sunday.
Among the latest developments are:
Man and woman found dead in the rubble of a house in Hounslow which exploded after a falling tree hit a gas pipe
A crane near Downing Street fell onto the Cabinet Office, causing Nick Clegg to cancel a press conference due to be held there
Dungeness B nuclear power station shut down both of its reactors after storm debris caused a loss of power
David Cameron raised concerns that trains had been cancelled too quickly, saying: "We will be able to look back and see whether people made the right decisions"
Virtually no trains in the south of England during rush hour, with severely limited service afterwards
220,000 homes suffered power cuts as winds of almost 100mph battered the South West, South, South East, the Midlands and the East of England
More than 130 flights cancelled from Heathrow and four at Gatwick, with Gatwick and Stansted Express train services also cancelled
Port of Dover had to shut and ferries coming from France, carrying 450 people, forced to wait at sea
Waves crash against a lighthouse at Newhaven during storms that battered Britain on Monday (Reuters)
Dungeness B nuclear power plant in Kent automatically shut down its reactors after debris blown by hurricane-strength winds fell onto its power lines and led to a loss of supply.
It could be up to a week before the two units at the plant one of Britain's nine nuclear power stations are up and running again.
But a spokeswoman for EDF Energy, which runs the site, said she hoped energy would be restored much sooner and that the public should "absolutely not" be concerned by the shut-down.
The two reactors shut down safely and diesel generators within the site were providing power for essential systems to continue to operate, Sue Fletcher of EDF said.
The strongest gust of wind in the storm - which has been dubbed 'St Jude' as it arrived on the saint's feast day - was recorded at 99mph on the Isle of Wight. The Environment Agency said there were 12 flood warnings in place across the South West, the Midlands and the East of England.
Emergency services at a house in Hounslow where a tree collapsed causing a gas main to rupture (Splash)
Rail companies said disruptions were likely to last well into the day, with some, including Stansted Express and Greater Anglia, saying they would be unable to run services until at least 12 noon.
Although the Kent port of Dover was reopened, P&O Ferries warned of delays of up to two hours on some sailings.
A commuter jumps over a fallen tree on his way to work (Reuters)
A double-decker bus "rolled over" in Suffolk, injuring the driver and several passengers.
Witnesses told police the vehicle blew over at 8am, rolling onto its side and coming to a stop in a field in Hadleigh.
The driver, a man in his 40s, was initially trapped and was treated at the scene by paramedics.
A police spokesman said: "He was suffering from neck pain, had taken a bash to his head and was in and out of consciousness.
"There were several other people on board, with a couple of walking wounded. We believe the driver has been taken to hospital. The road is completely blocked."
In central London, Whitehall was closed both ways between Parliament Square and Horse Guards Avenue after a crane collapsed on to the roof of the Cabinet Office. Nick Clegg was forced to cancel a monthly press conference following the incident.
During a visit to the Mini plant in Oxford, Prime Minister David Cameron said: "Any injury or loss of life is hugely regrettable.
"We have to make sure the emergency services can act as fast as they can to help people."
The path of the storm largely followed the route predicted by the Met Office, with hurricane-strength winds hitting the South West of the country in the early hours of Monday morning before moving up the south coast and to the Home Counties.
From there it blew across to East Anglia and was moving out towards the Netherlands shortly before 11am.
Forecasters predicted winds exceeding 80mph a maximum of 12 on the Beaufort scale and so they proved to be, with the strongest wind on lands recorded at Langdon Bay, Kent, at 82mph.
The second fastest wind was in Andrewsfield, Essex, at 79mph followed by Maston, Kent, at 70mph.
A car is trapped underneath a fallen tree branch blocking the road in St John's Wood (LNP)
Michael Fish, who famously failed to predict the 1987 storm, hailed the accuracy of new computer models which he said had helped prevent "horrendous loss of life."
The veteran forecaster, who had earlier advised commuters to take two or three hours off work if gales were affecting their areas on Monday morning, revealed the storm had ripped trees up from his garden.
"I had a phone call from my wife not so long ago and of course it was my fault that a tree has apparently gone down in my garden and over the neighbour's garage," he told BBC Radio 4's Today programme.
"So even I don't escape and I can hear some of you saying 'serves him right!'"
Asked if the scale of the storm had been overplayed this time, he said: "No, no. It's been a terrific storm.
"There has been massive damage and if we hadn't been banging the drum for about a week or so there could have been some horrendous loss of life as well.
"I am hoping and praying that we have virtually avoided all that."
The disruption from today's storm prompted a deluge of Tweets, many from those affected by rail cancellations.
While hundreds took to Twitter to post messages suggesting the predicted chaos had been over-hyped, others took a different view:
Tens of thousands of people heading to work from within London on Monday morning also saw their commute affected.
Seven Underground lines were part-suspended because of debris from the storm on the tracks, while no Overground trains ran until mid-morning and only then with severe delays.
There were even reports of drivers stopping their trains and going to collect branches that had gathered on the tracks themselves.
London Mayor Boris Johnson chaired an emergency meeting with the agencies working to clear the transport backlog in the capital.
"Clearly this has been a difficult night for many Londoners, and continues to be an incredibly trying morning," he said in a statement.
"Transport for London, the boroughs and the emergency services are working flat out in an effort to keep London moving and minimise disruption as far as is possible.
"I want to thank all the agencies for their professional response in incredibly testing conditions, and I'd urge Londoners to check before travelling by going to tfl.gov.uk for the latest information."
And the damage caused by the storm was not limited to the UK.
Twelve departments in the north of France were affected by the hurricane-force winds, according to national newspaper Le Figaro, with 75,000 homes experiencing a loss of power.
Rail services between Rouen and Paris were completely suspended in both directions after a train carrying 800 people broke down in a tunnel, leaving passengers trapped in the dark for four hours.
Two ferries carrying more than 450 passengers across the Channel to Dover were left waiting outside the port before it reopened shortly after 9am, Agence France Press reported.
The Netherlands, where the storm continued from the east coast of Britain, was placed on red alert for extreme weather.
A woman was killed in Amsterdam by a falling tree, local police said. The city's central rail station was also closed because of the strong winds.
And a ferry carrying 1,000 people from Newcastle to the Netherlands was forced to return to sea after the storm caused officials to close the port of IJmuiden, near Amsterdam.
The ship left the north east of Britain at 5pm yesterday and was due to reach the Dutch capital at 9.30am today, according to DFDS Seaways.
The ferry, which is believed to be waiting outside the port, is now expected to dock at 3.30pm local time.