Police were called to take witnesses away from the scene.
The Sun reported that Sam had been bullied and would sit on his own in the playground at lunchtime.
A family friend reportedly told The Sun: "Sam was being bullied at school but I don't know how, lots of children are bullied but it must have been horrendous for him."
One boy told the Daily Mail: "It's horrible. I have friends who were there and saw the whole thing.
"Some of the older pupils were really good – they held everyone back and made sure everyone else was safe.
"They said he was being bullied. It's only four days until school breaks up and you'd have thought he'd be able to get help."
Deborah Barrett, first wife of Sam's father James, told the Daily Mail: "It's just so sad. It's so awful. My three girls are Sam's half sisters, they are all so upset.
"It's horrible. You can't imagine, can you?
"He was a sensitive little soul, a cute little thing who was into gaming. He was funny and sarcastic with a great sense of humour."
Deborah added: "This is so horrible for the family. They loved him, they were all quite close.
"There were six kids altogether, they are all quite close, the children, and Sam was the youngest."
Meanwhile, floral tributes to Sam have been pouring in to the station, with one reading: "So sorry that life wasn't kinder to you sweetheart. RIP Angel."
Another note read: "R. I. P little man. Find your happiness in heaven."
The owner of a shop opposite the station descibed the scene after the incident.
"It was so sad. Children were running around crying and screaming," the shop owner said.
"One young girl came in the shop in tears and was screaming, 'I've seen it all'.
"We looked out and saw the train on the platform and put two and two together.
"The kids on the platform didn't know what to do."
A school spokesman told the newspaper they had "no record" of the teen being bullied and couldn't make any further comment.
Principal James Kibble said the school was "devastated" and it would be holding a series of assemblies to help students come to terms with the tragedy.
He wrote: "We were devastated to find out that, following an incident at Chertsey station, one of our year nine students died this afternoon.
"This is an incredibly difficult situation for everyone, but knowing the faith, compassion and strength of our school community, I am confident that we will work together to support one another.
"This will start from first thing tomorrow, and will be holding a series of assemblies to talk to the students about what has happened and how we can collectively come to terms with this tragedy.
"We would ask that our community joins together to remember the student and their family in their prayers at this incredibly sad time."
Police said the incident was not being treated as suspicious.
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.