A man has been arrested after a father was stabbed to death in front of his son and horrified passengers on a London-bound train, said British Transport Police (BTP) on Saturday.

Police had been called to Horsley station in Surrey about 1300 GMT on Friday after a 51-year-old man was knifed on the train traveling from Guildford in Surrey to London Waterloo.

Local media reported that a 27-year-old woman was also arrested on suspicion of assisting an offender.

"This is a fast-moving investigation and I am pleased that overnight we were able to arrest a man following a huge amount of police enquiries," said BTP Detective Chief Inspector Sam Blackburn in a statement on its official website.

"The investigation is moving with good progress and we are now confident to say that this is not believed to be a random assault," he said. "In the moments leading to the violent killing, both men appeared to be involved in an altercation lasting three minutes. Nothing justified the extraordinary violence that followed, and we are concentrating our efforts on the ongoing investigation."

The incident took place after a security guard and a woman were stabbed to death in separate cases in London on New Year's Day.

The number of killings in London in 2018, including murders, manslaughters and self-defense killings, rose to its highest level in the past decade.