Around half of services to London out of Brighton have been cancelled because of major flooding at Patcham, near Preston Park.
Tim Shoveller, Managing Director of SWT has written to all passengers to explain what the rail operator is doing to keep services running.
Like most rail companies across the ITV News Meridian region, Cross Country trains are also affected by the severe weather conditions.
No trains ran on Sunday between Leamington Spa and Banbury due to a landslip. Chiltern Railways advised customers north of Banbury to use Virgin Trains between London Euston and Birmingham New Street.
Chiltern Trains plan to run a normal timetable on Monday, 17 February but will need to pass the area at a reduced speed.
FGW is planning to run a near normal service on high speed routes into and out of London on Monday with the exception of the route closures at Dawlish, and between Bridgwater and Taunton. Buses will run on those routes that are closed.
Local services will also be running between Reading and London on Monday, although because of the flooding affecting signalling equipment near Maidenhead, there will be a small number of trains that we won't be able to run.
Mark Hopwood, First Great Western managing director, said:
– Mark Hopwood, First Great Western
This is great news for our passengers, who have faced a very difficult period of travel. We are finalising a new amended timetable, which we will publish through our online systems later today. To help customers who postponed journeys last week, ticket restrictions remain lifted until Monday. Customers are strongly advised to check our website before setting off in the morning."
First Great Western (FGW) and Network Rail plan to restore the majority of services into and out of London Paddington from Monday.
Network Rail's engineering and maintenance teams have been working to try and solve the problems caused by the flooding at Maidenhead that had affected the normal signalling system reducing service to just 20% of normal capacity.
Through a series of innovative engineering solutions, from start of service on Monday, in excess of 75% of normal services will be running.
Saturated ground could lead to flooding around Croydon, Hambledon, Basingstoke and Lower Farringdon in Hampshire.
Peter Willison, of the Environment Agency (EA), told a Whitehall briefing: "We are likely to see more severe flood warnings along the south coast representing the risk from very strong and big waves.
"The rainfall that we will see today, that will bring river levels back up on the Thames and we expect levels on slow responding rivers like the Thames, like the Severn, to stay high for a number of days to come.