We have been treating the third rail in the south of England with anti-icing solution and trains were running around the network overnight to keep the rails clear of ice as much as possible.
Additional people were used on the ground to respond to incidents and carry out regular inspections of the infrastructure.
We will continue to work closely with train operators throughout today to deliver the best possible level of service and apologise for any disruption caused to passengers.
For the latest information, passengers should check with National Rail Enquiries or their train operator before travelling.
More top news
Monday night's weather with Simon Parkin
Monday afternoon's weather with Simon Parkin
Monday's weather with Simon Parkin