Many train services remain suspended on Saturday and “do not travel” notices are in place for some routes.
South Western Railway expects “significant disruption” across its network throughout the day, and said work was ongoing to clear the lines after more than 40 trees were felled on its routes.
Several Great Western Railway services have returned, with other operators able to run a partial service, but some long-distance routes are still facing suspension.
Routes on the Greater Anglia and Stansted Express network have also been suspended due to fallen trees.
Meanwhile, Southeastern said a train, which was not in service, hit a fallen tree just outside Longfield station in Kent.
Transport Secretary Grant Shapps said services are gradually returning to normal but warned travellers to expect further disruption this weekend.
He told the BBC: “Trains are in the wrong locations, debris is still being removed from our roads, airports are expected to be very busy – people catching up with flights – and potentially queues at ports. Expect disruption, do check before you travel.
“We’re still on a yellow warning today as well, so still windy out there, but things are returning to normal.”
National Rail said many operators were reporting “major damage” to the railway and obstructions on the line and urged passengers to check before travelling.
It said: “Network Rail have additional engineers out across the network dealing with the continuing problems, and will check all affected lines for damage before reintroducing services as quickly as possible.”
Jacqueline Starr, chief executive of industry membership body the Rail Delivery Group said: “In the aftermath of Storm Eunice, our people are working hard to get the railway back up and running. There will still be some disruption this weekend so we are urging people to check before they travel.”
It comes after Storm Eunice caused travel chaos across the UK on Friday, with hundreds of flights cancelled, rail lines blocked and road bridges closed.
More than 430 flights due to take off or land at UK airports were cancelled on Friday, while the M4 Prince of Wales Bridge and the M48 Severn Bridge, which link England and Wales across the River Severn, were closed due to high winds.
The M4 Prince of Wales Bridge has been re-opened on Saturday, but the M48 Severn Bridge remains closed in both directions.
A spokesman for the Severn crossings said the bridge would not reopen until a detailed inspection had been carried out on Saturday morning.
The Port of Dover was closed “in the interests of customer and staff safety” on Friday, meaning no ferries could operate between Dover and Calais.
It has since re-opened to shipping and some ferry services have resumed, but passengers are advised to check before travelling.
The Queen Elizabeth II bridge, which is part of the Dartford Crossing, was closed on Friday but, as of Saturday morning, has reopened.