Police said they were also investigating whether there were any links between those incidents and a stabbing in the suspect's hometown of Peterborough the previous night as well as two other incidents there.
Eleven people were injured in the mass stabbing on the London-bound train, including a member of the train crew hurt while trying to stop the attack who was still in hospital on Monday in a critical but stable condition.
Anthony Williams, a 32-year-old UK citizen, appeared at Peterborough Magistrates' Court on Monday and was remanded in custody until his next court hearing on December 1.
Prosecutors charged him with 11 counts of attempted murder, one count of assault occasioning actual bodily harm and two counts of possession of a bladed article.
Ten of the attempted murder charges were linked to the train attack, British Transport Police said, while the eleventh was connected to the incident at the London station.
Police have ruled out terrorism and said the suspect acted alone.
Williams was arrested when the train made an emergency stop in the town of Huntingdon, about 120km north of London.
Police say he was detained within eight minutes of officers receiving the first emergency calls.
The minutes-long stabbing spree spread fear and panic through a train bound from Doncaster in northern England to London on Saturday evening.
The train was about halfway through its journey and had just departed from a stop at Peterborough when police began receiving calls about people being stabbed onboard.
The most seriously wounded victim is a member of train staff who tried to stop the attacker and suffered "grievous injuries," Home Secretary Shabana Mahmood said.
"On Saturday he went to work to do his job. Today he is a hero and forever will be," Mahmood told MPs in the House of Commons.
Police said they were investigating whether other incidents involving a man with a knife in Peterborough were linked.
"British Transport Police retain primacy for the overall investigation, which will include these three incidents," Cambridgeshire Police said in a statement.
Officers attended the stabbing of a 14-year-old, who sustained minor injuries, in Peterborough on Friday night but could not locate the offender, they said.
A man also appeared with a knife at a barber's shop in the south of the city on Friday night, and police were called to the same place on Saturday morning.
Scunthorpe United, an English fifth-tier football team, said their player Jonathan Gjoshe was one of the victims of the attack and he remained in hospital with non-life-threatening injuries.
Transport minister Heidi Alexander said on Monday the suspect was not known to security services.
She declined to comment on whether he was known to mental health services.
Five of the injured had been discharged from hospital by late on Sunday.
Authorities said the attack was an isolated incident but stepped up security on the railway, with armed police officers on patrol on Monday at major train stations.
The government rejected calls for increased security measures such as airport-style passenger and baggage screening to be introduced at the United Kingdom's 3500 railway stations, saying that would not be "proportionate or practical".
with AP
