He said the watchdog recognised the efforts made under “extreme circumstances” to keep passengers safe and help them complete essential journeys.
“Any passengers who heeded advice not to travel should claim delay repay compensation in order to get their money back, including those using a season ticket,” he added.
“People whose journey was severely disrupted should also keep receipts for all unexpected costs that arose from their efforts to complete their journeys yesterday, and contact their train operator to claim not just for their delay but any additional expenses they incurred.”
Trains continued to be affected on Saturday morning despite power bring restored.
Cancellations and amended timetables were expected on services operated by Great Northern, Grand Central and LNER. Travellers at Kings Cross experienced ongoing problems.
Tom Moran, Managing Director of Thameslink and Great Northern, said on Saturday: “Thameslink services are back to normal, however the knock-on effect from last night is causing ongoing issues on Great Northern.
“We have trains in the wrong locations and drivers who worked a lot of extra hours.
“This reduces availability for today which will unfortunately cause more cancellations.
“Replacement buses and extra staff are in place at key stations to help our customers.”