Southern Railway and South West Trains have both warned of cancellations and disruption ahead of the approaching storm.
Southern said it was "highly unlikely" it would run services early on Monday morning.
The train operator, which serves Sussex, Kent, Surrey, Hampshire and London, said it had been advised that "trees and other debris may fall on and obstruct railway lines".
Storm clouds gathering over Brighton earlier Pic: Phil Beaven @beevr001An amber weather warning has been issued across large parts of England and Wales as a hurricane-strength storm builds over the Atlantic and moves towards Britain.
A Southern statement said: "As a result of this, we will not be running any services tomorrow until the storm has passed our region, and Network Rail has been able to assess any damage from the storm and confirm that lines are clear of debris."
"It is therefore highly unlikely that we will run any services before at least 0900 tomorrow morning.
"And even when we are cleared to run, the first services will be very disjointed given the difficulties in getting trains and their crew to the right locations."
South West Trains has warned people not to travel at all on Monday and said it would be running a "significantly reduced timetable ... with the majority of services not expected to run until at least 0800".
Rough seas at Porthleven, CornwallIt said trains across its network would be running slower than normal and observing a 50mph speed limit in case of debris on the track.
South West services, such as the route between Salisbury and Bristol, have already been cancelled.
Some have the compared the approaching storm to the Great Storm of 1987, when 18 people died and thousands of homes were without power for several days.
Veteran weatherman Michael Fish famously failed to predict its severity before it flattened trees, knocked out power and left 22 people dead in England and France.
This time he has warned people to "batten down the hatches" and to delay their journey by two or three hours on Monday morning.
The storm will intensify very quickly when it reaches the UKHe told Sky News' Murnaghan show: "There is certainly a severe storm on the way - and we certainly do need to worry about it.
"If you draw a line from about Aberystwyth to the Humber - everywhere south of there looks like getting affected by strong winds, to the north of that the problem is going to be heavy rain and localised flooding.
"These strong winds aren't going to last all that long, but they are going to be unfortunately getting up around about rush hour time, so the message we're trying to convey at the moment is to delay your journey just by two or three hours in the morning, and then you should be safe."
His comments were echoed by senior fire chiefs who have urged people to stay indoors if possible, and to take extra care if venturing out.
Meteorologists have warned the fierce winds of up to 80mph and torrential rain could leave a trail of destruction, damaging buildings and bringing down trees and power lines.
Roads may also be hit by flash flooding, bringing rush hour traffic on Monday morning to a halt, and homes could be flooded.
An amber warning is in place across the southern half of England and WalesPrime Minister David Cameron said he had chaired a call with Government departments and agencies to hear about their plans to "ensure people are protected from tonight's storm".
He was updated on preparations and contingency planning for transport, schools. hospitals, councils and power supplies.
Mr Cameron was told that the storm could have "a widespread impact", but that transport providers, local Government, emergency services and power companies had plans in place to respond.
The much-anticipated storm - which the Met Office has said will affect Britain on Sunday night and Monday morning - has been named St Jude after the patron saint of lost causes, whose feast day is tomorrow.
Insurance companies have advised households to take steps to protect themselves and their property.
People should also establish evacuation plans, place valuable items upstairs to limit flood damage and ensure gutters are clear so water can drain away.
The Environment Agency says 20-40mm of rain could fall within six to nine hours.
It has been compared to the Great Storm of 1987It has teams working to minimise river flood risk, clearing debris from streams and unblocking culverts, and are closely monitoring water levels so they are ready to issue flood warnings if necessary.
A spokesman said: "Seafronts, quaysides and jetties should be avoided due to the risk of overtopping by waves and wind-blown shingle."
Severe weather alerts are in place, with an amber warning, meaning "be prepared", for the southern half of England and Wales.
A yellow warning, meaning "be aware", has been issued for the rest of Wales and England up to the border with Scotland.
Ferry services between Plymouth and Roscoff, as well as Penzance and the Isles of Scilly, have been cancelled.
Brittany Ferries, which runs the Plymouth-Roscoff route, said on its website: "We are in the process of contacting all passengers booked on these sailings. We apologise for the inconvenience the cancellation of these services will cause."
Sky News weather presenter Jo Wheeler said: "The storm is coming through at the worst possible time; from around midnight to midday on Monday.
"So Monday morning's rush hour looks like being chaotic with travel and power interruptions anticipated.
"The public are advised to take the greatest care - and to carry a fully charged mobile if travel is necessary.
"Winds gusting at 80mph are quite capable of bringing down trees and power lines and causing structural damage.
"Trees are still full in leaf at this time of year and the ground is quite damp so there is more chance they can be ripped from the ground, and branches ripped from trees."
She said Atlantic storms of this type usually develop further west across the ocean, losing strength by the time they reach the UK and Ireland.
But the storm is expected to intensify near to the mainland before it hits the south-west coast with full force and sweeps north-east across the country, with a strong jetstream and warm air close to the UK contributing to its development and strength.
Darron Burness, head of the AA's flood rescue team, said: "The timing couldn't really be worse, potentially causing significant travel disruption on Monday morning, which is one of the busiest times on the roads."
The Metropolitan Police has urged people to avoid calling 999 during the storm unless there is a real emergency.