Gusts of up to 88mph - the tail end of Hurricane Gonzalo - hit Oban in western Scotland, while most of the UK saw strong winds.
About 10,000 passengers were affected by flight cancellations at Heathrow, and several UK ferries did not sail.
The woman died in central London, with a man hurt in a nearby incident and three people injured in West Sussex.
Gonzalo caused widespread damage and a power blackout when it hit the island of Bermuda last week, with winds of up to 110mph.
The strongest winds in the UK were recorded mainly in northern parts of the country and in Wales.
Fallen trees caused problems on the roads, and there were delays and cancellations on several train routes.
In other developments:
Scotland Yard confirmed the woman in Knightsbridge died after she was hit by a tree brought down by high winds.
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."
The severe weather caused some travel disruption with flights cancelled at Heathrow, but other airports reported no major problems.
BBC Weather said Wednesday would be much quieter.
In central London, paramedics were also called to reports of a tree falling on a person at about 12:20, in Belgravia.
A London Ambulance Service spokesman said: "We treated a man reported to be in his 30s for leg, chest and head injuries. He was taken as a priority to St Mary's Hospital Paddington."
The three people hit by a tree in Southwick, West Sussex, were taken to hospital but paramedics said there was "nothing to suggest serious injury".
That tree fell at about 10:00 in Shelldale Road. South East Coast Ambulance Service said 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.
Heathrow said 110 flights were cancelled and that figure included Lufthansa flights disrupted by a pilots' strike. This was less than 10% of its usual daily total of about 1,286 flights.
Among other UK airports, Gatwick said there was no disruption, Stansted said it operated "normally" and Manchester said its only cancellations had been due to issues at other airports, mostly Heathrow.
Edinburgh Airport said its only cancellations were three flights to Heathrow, and Glasgow Airport said its flights had run as normal.
There were no reports of widespread train delays, but South West Trains tweeted that it had seen "poor rail adhesion" - meaning "trains have had trouble accelerating as the wheels slip when applying power".
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.
A woman has died and four people were taken to hospital after winds felled trees and caused widespread disruption.