West Coast Railways (WCR), which carries 85,000 tourists a year on the route, was barred by Network Rail last month from operating across Britain after causing the worst case of running through a red light this year.
WCR had planned 225 trips for the service, made famous by the Harry Potter films, until October. It has run the Jacobite for 20 years.
However, the company’s operating permit was suspended after another of its steam trains ran past a red signal and stopped across the Great Western main line near Swindon in March, less than one minute after an express train.
Network Rail said: “The operations of WCR are a threat to the safe operation of the railway”.
WCR has been given until Friday, 15 May to make a series of improvements.
WCR spokesman David Pitts said: “We have only until Monday, the start of the Jacobite season, to regain our track access.
“Failure to do so will be a bitter blow to all passengers and people relying on the service locally for an income.
“At this stage, it’s looking unlikely. We expect to decide tomorrow whether services will start on Monday.
“Everything that can be done is been done to keep this historic service alive.
“In the event of us having to cancel a Jacobite service, all passengers will be given at least 48 hours’ notice and full refund, but we sincerely hope it doesn’t come to that.”
Mr Pitts said DB Schenker, the only firm which could run the Jacobite on its behalf, had shown no interest.
ScotRail had also planned to use WCR to run a series of steam specials across Scotland from 20 June but it is now seeking another operator.
A Network Rail spokesman said: “Network Rail has not taken the decision to suspend WCR lightly, but our number one priority is safety.
“We are in discussions with WCR and will continue to work with them to address the safety concerns that we have raised.”
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