Almost the whole of the UK is under amber weather warnings for strong winds from Storm Isha.
Met Office amber wind warnings are in force or all of the UK apart from London and parts of the South East since 18:00 on Sunday.
Gusts of up to 80mph (128km/h) are expected, posing a risk to life. The Met Office said it was rare for all of the UK to be under such an alert.
BBC Weather’s Matt Taylor said the disruption will continue into Monday.
Two amber warnings are in place from 18:00. One stretches across central, eastern and western England and all of Wales.
The other covers all of Scotland, northern England and Northern Ireland.
The Republic of Ireland’s weather service Met Éireann has issued a red warning – its highest – for wind in the north-west of the country.
It said Isha would bring “severe and destructive gusts, particularly in coastal and exposed areas”.
BBC Weather’s Matt Taylor said “widespread gales” are expected across the UK by the end of the day.
Gusts of 50 to 60mph will be felt widely across the UK with 70 to 80mph around some coasts. At Capel Curig, Snowdonia, a wind gust of 90mph was recorded on Sunday afternoon.
Additionally, there are yellow warnings for rain that cover the whole of the UK including London and parts of the South East not subject to the amber wind alerts.
Disruption could continue well into Monday’s morning rush hour.
Mr Taylor added that Storm Isha was a low-pressure weather system that brought heavy snowfall to the north-eastern US at the end of last week, and has developed as it crossed the Atlantic.
The Met Office said that there was a good chance of power cuts, which could affect mobile phone signal in affected areas, while roads and bridges are likely to be shut. Rail and bus services could face delays and cancellations.
It continued that there was a risk to life in coastal areas from large waves and debris being blown inland.
As part of wider guidance, it has also warned people to minimise risk by staying away from windows whilst at home.
There is also potential for “the odd isolated tornado” to hit western parts of the UK, Met Office forecaster Marco Petagna said.
Passenger and freight services across Scotland will be suspended from 19:00 on Sunday, with ScotRail saying there will also be no rush hour services on Monday morning.
Network Rail is also imposing 50mph speed restrictions across England and Wales as a safety measure, to keep trains safe from falling trees and debris on the track.
It added the restriction will “result in fewer services with elongated journey times”.
Rail companies including Avanti, LNER and Transpennine said the storm would affect their services and warned customers not to travel on Sunday.
Southeastern has cancelled early Monday morning trains before 06:00 into and out of London to allow engineers to check for debris.
Other rail lines are advising travellers to avoid travelling during the storm.
British Airways has cancelled a number of flights and has apologised to customers for disruption.
The carrier said: “British Airways said: “Like other airlines, we have had to make schedule adjustments due to the adverse weather conditions across the UK and Europe caused by Storm Isha.”
Ferry companies meanwhile announced a series of cancellations. Irish Ferries said sailings between Holyhead and Dublin and between Pembroke and Rosslare were cancelled.
DFDS meanwhile said Dover, Calais and Dunkirk services were operating with delays, and the service between Newcastle and Amsterdam was also likely to face delays.
A spokesman for the Energy Networks Association, which represents Britain’s operators, said on Friday: “An amber warning brings an increased risk of damage to homes and vital infrastructure.
“Energy network operators are preparing to deal with any damage quickly and safely.”
The heaviest downpours may occur on Sunday as 30mm-50mm could fall in many places – and there is potential for peaks of 80mm-100mm over hills.
The Met Office has said heavy rain could lead to flooding this week. As of 12:00 on Sunday, the Environment Agency had issued eight flood warnings, where flooding is expected in England, and 59 flood alerts, where flooding is possible.
After days of freezing temperatures and snow in some parts of the UK, higher temperatures are expected by the end of the weekend – but the Met Office has warned it may not feel warmer due to high winds.
Storm Isha follows Storm Henk, which hit the UK earlier this month, causing flooding and disruption, and is the ninth named storm since September.
The Met Office names storms when they have the potential to cause disruption or damage. The agency says it is easier for people to follow the progress of a storm on TV, radio or social media if it has a name.