The Carnforth-based company operates charter trips on the picturesque Settle to Carlisle line, which runs through the Yorkshire Dales, as well as, among others, a route taking in Fort William in the Highlands.
WCR owns the Hogwarts Express engine featured in the Harry Potter films that last month went on display at Warner Bros Studio Tour in Leavesden, Hertfordshire.
The suspension notice means it cannot run chartered services until 15 May.
Network Rail said the decision had not been taken lightly.
According to Rail magazine, it is an "unprecedented suspension" as, since privatisation, operators have been barred from certain routes but never hit with a total network ban.
A Network Rail spokesman said services were suspended from 00:00 on 3 April and would only resume if seven action points are addressed.
The spokesman said: "We have set out a number of actions to address the safety concerns raised and will continue to work with WCR to ensure their services can run safely in future."
The action points include:
- Introducing an "effective, risk-based driver monitoring regime"
- Reviewing procedures to make sure drivers understand all safety and operational information
- Establishing a plan with a deadline to implement actions from Network Rail's January review of the company's safety policies
Network Rail's suspension notice said it "ranked as the most serious Spad that has taken place this year when the industry risk ranking methodology was applied".
It said it happened near junction SN45 at Wootton Bassett in Wiltshire on 7 March when a WCR service between Bristol and Southend overshot a busy junction.
The Rail Accident Investigation Branch (RAIB) is investigating.
Network Rail said the response from West Coast Railways was "inadequate", in a meeting held on Tuesday.
Sources: Rail Magazine, CNS, BBC, Network Rail
JULIAN BRAY ++44(0)1733 345581, Journalist, Broadcaster, Aviation Security & Operations Expert, Travel / Cruise Industry, EQUITY, NUJ, Broadcast COOBE ISDN ++44 (0)1733 345020 (DUAL CODEC) SKYPE: JULIAN.BRAY.UK e&oe Cell: 07944 217476 or iPhone 0743 530 3145 #VENDOR 10476453 http://feeds.feedburner.com/BraysDuckhouseBlog