Network Rail says it is hopeful that the last part of the Tarka line between Barnstaple and Crediton, which was closed by flooding, will reopen on Monday 7th January.
Divers are expected to inspect the foundations of two bridges near Umberleigh on Saturday morning.
The section of the line between Exeter St Davids and Crediton is already open.
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The Post Office said it was 'business as usual' but unions said Saturday's industrial action was getting solid support.
Workers and managers are to stage another strike on Saturday amid a long-running dispute over jobs, pensions and closures.
Cloudy in the West with a few showers. Sunny in the East but cold.