Passengers said the famous locomotive came to a “shuddering stop” near St Neots, Cambridgeshire, and Virgin Trains East Coast warned that other services were being delayed by up to 15 minutes due to photographers on the track.
Footage filmed from the stationary train showed people walking down the line holding cameras.
British Transport Police received reports of around 60 trespassers on the track near St Neots shortly after 9am. No arrests were made.
Network Rail (NR) issued an urgent plea to spectators to stay safe and confirmed that Flying Scotsman was held up for 10 minutes before continuing the journey at a reduced speed.
An NR spokesman said: “The number of people beside the track is already giving us safety concerns and means we are having to slow trains down.
“Trespassing on the railway is illegal and incredibly dangerous. Please help us to make today a success and stay off the railway.”
The Rail magazine’s editor Nigel Harris, who is on the train, said Flying Scotsman was forced to carry out a “big brake” before coming to a “shuddering stop”.
He described the incident as “rampant trespass by mindless hordes”.
Some 297 VIPs, fundraisers, competition winners and members of the public who paid up to £450 each are on board for the trip.
• READ MORE: Video: Flying Scotsman embarks on inaugural journey
Hundreds of people who arrived at London King’s Cross from 6am to secure a vantage point on platform one were covered in steam as the journey began.
Built in Doncaster, South Yorkshire, in 1923, Flying Scotsman soon became the star locomotive of the British railway system, pulling the first train to break the 100mph barrier in 1934.
It has been painted in the traditional early 1960s British Rail green for its first official outing bearing its nameplates after the restoration project.
Michael Portillo told the Press Association he was “very excited” to be travelling on the train as part of filming for BBC documentary series Great British Railway Journeys.
“This is certainly the most famous journey and most famous locomotive in Britain,” he said.
Mr Portillo described Flying Scotsman as “an engineering triumph” and praised its designer, Sir Nigel Gresley, for having “an eye for engineering, for design, for style and for marketing”.
The National Railway Museum (NRM) in York bought the locomotive for £2.3 million in 2004 before work got under way on its restoration in 2006.
The museum’s director, Paul Kirkman, said Flying Scotsman was a reminder that “railways have been making this country run properly for nearly 200 years”.
He said the restoration project was a “long old journey” but added that it was “incredibly satisfying” to see the locomotive returned to service.
Also among the passengers was Ron Kennedy, who drove Flying Scotsman from 1956 until it was retired in 1963.
The 83-year-old, from Leigh-on-Sea in Essex, beamed with delight as the locomotive pulled into the station he first worked at as a cleaner almost 70 years ago.
“It’s unbelievable. I never dreamt about being on it again. To be out with it is just fantastic,” he said. “It was a good engine.”
Flying Scotsman will be kept at the NRM until March 6 before embarking on a tour around the country.