Heathrow Express services have also been cancelled.
In a tweet, Great Western Railway said: "Important update. Paddington Station will close from 0800 on 01/03/18 owing to severe weather conditions. All High Speed Services will start and terminate at Reading."
Hourly trains will run from between Reading and Bristol Temple Meads.
National Rail tweeted: “London Paddington station is CLOSED.
“Long distance trains will not run between Reading and London Paddington.
“Local stopping trains will not run between Ealing Broadway and London Paddington.”
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Police push a car on the on the M80 Haggs in Glasgow
The rail operator added tickets will be accepted on other routes.
Angry passengers have been tweeting about the disruption.
@thompson_doug, posting a photo of a screen explaning the closure was due to "slippery, icy platforms" wrote: "Seriously? This is the reason Paddington is closed? Well, thats embarrassing for a station with a roof."
TWITTERPaddington Station closed - all services are terminating at