The 42-year-old, who was one of five suspects named over the 1993 racist killing, was punched to the ground by a black inmate just nine days into his sentence.
Acourt was banged up for nine years this month for masterminding a multi-million drugs racket.
According to a source, he has been moved to a cushy segregated section at HMP Wandsworth following the attack.
The luxury move means he has access to a kitchen where he can cook his own meals and can play games in a room with a 50inch HD TV.
The source said: "Acourt was attacked by a fellow inmate last week so he was moved by prison staff.
"He was in one of the main wings before. Now he's living a top luxury lifestyle.
"It's shocking. Acourt is let out of his cell at 8am and can live like a normal human being until 9pm at night.
"Others are barely even allowed for one hour a day."
The Sun revealed last week how Acourt was punched by hulking con Tyrone Archer, 39, who has now been put on report by governors.
Archer, from Croydon, South London, is understood to have lashed out at Acourt as he got ready to exercise with other inmates at Wandsworth.
Sources said Acourt instantly fell to the floor before prison officers intervened. Acourt did not need medical treatment.
Stephen was stabbed to death at a bus stop in Eltham, South London, 25 years ago in a sickening racist attack that shocked the nation.
Acourt was one of five men named as suspects and was caged for nine years on December 9 after he admitted his role in a multi-million pound cannabis smuggling operation.
His brother Neil Acourt, who helped him head up the smuggling gang and was also named as a murder suspect, is already in prison for drug dealing.
Two friends, Gary Dobson and David Norris, were finally convicted in 2012 – 19 years after the murder – and given life terms.
The fifth suspect – Luke Knight – is still living in Eltham less than three miles from where 18-year-old Stephen was stabbed to death.
Regarding the move, a Prison Service spokesperson said he couldn't comment on individual prisoners.
He added: "A prisoner at HMP Wandsworth has been put on report after punching a fellow prisoner on 12 December."
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