Southern Rail said engineers were advised of a failure of the electricity supply in the Arundel area shortly after 11am this morning (Monday, July 12).
Engineers advised that it will take approximately three hours to fix the fault.
Trains have been unable to move between Arundel and Barnham and also between Littlehampton and Worthing.
There have also been no trains running between Brighton/Hove and Littlehampton, Portsmouth and Southampton. No services have been running between Horsham and Bognor Regis, Portsmouth and Southampton.
'A very limited' number of buses have been running to keep passengers moving between Horsham, Arundel, Barnham, and Chichester.
"We are anticipating service disruption throughout the afternoon," a Southern spokesperson said.
"It is in your best interest to travel later today where possible. If you do decide to travel now, your journey time will be extended significantly."
The power failure to the signalling equipment meant no trains could run over Arundel Junction.
Signalling technicians installed a temporary back up power system to get trains moving again.
Southern confirmed that the power had been restored at Arundel by 3.10pm.
A spokesperson added: "However it will take some time to resume our West Coast services via Arundel.
"Please continue to allow plenty of extra time to complete travel this afternoon."