Trains have started to run between Huntingdon, St Neots and London.
First Capital Connect is running one train an hour to London Kings Cross leaving Huntingdon at 11 minutes past the hour and St Neots at 20 minutes past the hour.
An East Coast train is also departing Huntingdon for London, at 51 minutes past the hour.
Trains running to Peterborough call at Huntingdon at nine minutes past the hour. The next FCC train departing Huntingdon to Peterborough is at 5.22pm, and St Neots at 5.12pm.
A spokesman or FCC said: "We plan to run to the planned timetable tomorrow but some of our services may be shorter than normal and there could be late notice changes so we urge passengers to please check before they travel at www.firstcapitalconnect.co.uk or @firstcc."
Disruption is said to last on the Peterborough to Kings Cross lie until 2am tomorrow morning.
A statement on the train operators website said: "The storm have lead to fallen trees and damage to buildings and overhead lines. In the interests of safety, Network Rail has advised us not to operate any trains on our network from until it is safe to do so.
"We currently have no indication of when services will resume. Trees and over structures are blocking the railway at a number of locations. We are also unable to operate any replacement buses at this time."