BBC News Travel
Trains are not able to travel through Brockenhurst following a fire on board a train at the station.
British Transport Police said the "minor fire" on a CrossCountry train has been extinguished.
Services on the Southampton to Bournemouth line are expected to be disrupted until at least 14:00 GMT with rail replacement buses operating.
BBC Local Live
No CrossCountry trains are running between Plymouth and Exeter St Davids until at least 11:00, National Rail Enquiries says.
It said it was because of forecasted severe weather in the Dawlish area.
The move affects all stops on CrossCountry service between London Paddington and Penzance.
Passengers could use Great Western Railway services "on reasonable routes", it added.
A flood alert was issued for the area by the Environment Agency on Monday.