Stations including Fareham, Eastleigh and Southampton have been affected by adverse weather.
In a tweet Network Rail Wessex said: ‘We're experiencing intense rain and flash floods across the South East at present which are affecting our railway.
‘Teams of engineers are on the route and our pumps are working hard to manage the flow. Speed restrictions and cancellations have had to be put in place.’
And Southern Rail said: ‘Due to flooding at various points on the network, your intended train will be cancelled or delayed.’
People are advised to check rail companies’ websites before travelling.