The route between Haywards Heath and Lewes is closed.
Rail replacement buses are running between Haywards Heath and Lewes via Cooksbridge and Plumpton instead, Southern said.
A revised service is also operating between Brighton and Eastbourne/Bexhill.
Passengers travelling between Bexhill, Eastbourne, Lewes and London Victoria should travel via Brighton, Southern said.
Southeastern said its trains between London Cannon Street, London Charing Cross, London Bridge and Hastings are not running today.
Southern said its services between Ore, Brighton and Hastings and Ore and Ashford International are all shut as well, as engineering work is taking place in the Hastings area.
Replacement bus services are running between Bexhill and Ashford International, as well as between Battle and Hastings.
Due to limited road access, these buses will not stop at Crowhurst.
Passengers should change at Battle for a minibus service to and from Crowhurst.
So far this morning as of 9am the roads across the county are reported to be free of congestion.
A message from the Editor, Gary Shipton:
In order for us to continue to provide high quality and trusted local news, I am asking you to please purchase a copy of our newspapers.
With the coronavirus lockdown having a major impact on many of our local valued advertisers - and consequently the advertising that we receive - we are more reliant than ever on you helping us to provide you with news and information by buying a copy of our newspapers.
Our journalists are highly trained and our content is independently regulated by IPSO to some of the most rigorous standards in the world. But being your eyes and ears comes at a price. So we need your support more than ever to buy our newspapers during this crisis.
Stay safe, and best wishes.