Storm Darragh is bringing disruption to travellers and tens of thousands of people are without power.
Great Western Railway (GWR) said there were no services between Plymouth and Penzance until at least 16:00 GMT.
Nearly 21,000 properties are without power in Cornwall, along with nearly 17,000 in Devon said National Grid.
There was a 96mph gust at Berry Head near Torquay in Devon on Saturday, the highest wind speed recorded at that spot, said BBC South West forecaster Alex Osborne.
Many roads are still blocked by trees and a car was severely damaged by a fallen tree in Cornwall, but there were no injuries.
A yellow warning for wind remains in force across Devon and Cornwall and much of England and Wales until 18:00 GMT.
Gusts of wind are still hitting about 50mph (80km/h) in Cornwall and the Isles of Scilly, but the wind is expected to ease.
Cornwall Council said 180 fallen trees had closed 35 roads.
The Tamar Bridge between Devon and Cornwall remains closed to high sided vehicles.
Police dealt with a collision involving a car and a tree on the A39 at Perranaworthal in Cornwall on Saturday night, which left the car windscreen smashed.
No-one was injured and the road has been reopened.
Bude Leisure Centre in Cornwall remains closed because of roof damage caused by the storm.
The King Harry Ferry at Trelissick in Cornwall is closed because of high winds.
GWR has confirmed that the Barnstaple and Okehampton lines and Cornwall branch lines remain closed until at least 16:00 GMT and that the sleeper train to Paddington on Sunday night has been cancelled.
