The London Fire Brigade are working at the scene outside Hyde Park Barracks to remove the tree
A woman has died after being hit by a falling tree in high winds in London.
The tree fell opposite Hyde Park Barracks in Knightsbridge at about 11:00 BST.
Earlier, three people were injured by a falling tree in Southwick, West Sussex, though paramedics said there was "nothing to suggest serious injury".
The storm is the tail-end of Hurricane Gonzalo, which hit the island of Bermuda last week, and is causing travel disruption across the UK.
Gusts of up to 70mph have been recorded in north Wales and the Isle of Wight, and a Met Office wind warning is in place for much of the country.
Second man in hospital
A London Ambulance Service spokeswoman said: "We sent an ambulance crew, a responder by car, an advanced paramedic, a medical team from London's Air Ambulance by car and a duty officer to the scene.
"Sadly, despite our attempts to resuscitate the patient, a woman died at the scene."
Paramedics said they were called to Kensington Road in Knightsbridge at 11:40 BST where the woman died
In a separate incident, paramedics were called to reports of a tree falling on a person at around 12:20 BST nearby in Belgravia.
A London Ambulance Service spokesman said: "We treated a man reported to be in his thirties for leg, chest and head injuries. He was taken as a priority to St Mary's Hospital Paddington."
The storm has caused some travel disruption with flights cancelled at Heathrow. Other airports are reporting no major problems.
Fallen trees and high winds are causing problems on the roads, and there are delays and cancellations on many ferries.
BBC Weather said winds could be as strong as 60mph in England and 70mph in coastal parts of Northern Ireland and Scotland later.
The three people hit by a tree in Southwick included two women, but the sex of the third casualty has not been released.
That tree fell at about 10:00 BST in Shelldale Road, and South East Coast Ambulance Service said the two women were taken to Royal Sussex County Hospital, one with spinal pain and one with a head injury and pelvic pain.
The third patient was taken to Worthing Hospital.
A lorry overturned on the A1(M) south of Peterborough at about 05:30 BST, blocking all southbound lanes
Large waves hit the seafront at Blackpool, where gusts of 60-70mph were recorded
Heathrow says 110 flights have been cancelled so far and that figure includes Lufthansa flights disrupted by a pilots' strike. This is less than 10% of its usual daily total of about 1,286 flights.
Among other UK airports, Gatwick said it did not "anticipate any disruption", Stansted said it was "operating normally" and Manchester said its only cancellations by 09:00 BST had been due to issues at other airports, mostly Heathrow.
Edinburgh Airport said its only cancellations by 09:00 BST were flights to Heathrow, and Glasgow said its flights were running as normal.
There have not been reports of widespread train delays, but South West Trains tweeted that it was "experiencing poor rail adhesion" - meaning "trains have had trouble accelerating as the wheels slip when applying power".
Most train services are running as normal despite the severe weather, as seen here in Whitehaven, Cumbria
In other developments:
Other trees also fell in London, including this one in Southwark Street
Council staff worked to clear fallen trees, like this one in Rochford, Essex
Forecasters said there would be some sunshine as well as storm clouds, seen here over Bolton
Speaking from County Down, BBC Ireland correspondent Chris Buckler said the storm had been "rough enough" but had not hit "quite as hard as many had feared".
There had been high winds but not much disruption in Northern Ireland, he said.
Gonzalo caused widespread damage and a power blackout when it hit the island of Bermuda last week, with winds of up to 110mph.