The Daily Telegraph said officials have canceled numerous trains and buses due to impassable roads.
National Rail said "various routes" in the Southwest would be disrupted with "poor road conditions."
The Daily Telegraph said problems are affecting commuters attempting to return to work after Christmas, with 2012 set to be the wettest year on record.
There are currently no trains to Slough, Reading, Heathrow and London Paddington, and a "very limited" bus service is in place, the Telegraph said.
First Great Western warned passengers not to travel unless it is absolutely necessary.