Skirmishes broke out towards the end of the Hammers' 2-1 win on Wednesday, with police and stewards battling to keep supporters apart as coins, bottles and plastic seats were thrown.
There was a heavy police presence in place at the London Stadium, formerly the Olympic Stadium, which has seen repeated violence involving West Ham fans since they moved into their new home at the start of the season.
Both clubs condemned the violence soon after the match and on Thursday a joint statement issued by West Ham and the London Stadium revealed the number of spectators at risk of a stadium ban after officials had studied closed circuit television footage of the disorder.
"Banning notifications will be issued for offences ranging from the use of abusive and offensive language to missile throwing. In line with our zero tolerance policy, all those involved will receive a seasonal or lifetime ban depending on the severity of the offence."
Having intially said Thursday there had been seven arrests for public order offences, London's Metropolitan Police later corrected that figure to six.
Earlier, Tracey Crouch, Britain's sports minister, was among those calling for anyone involved in the violence to be given a life-ban.
"No-one wants to see a return to the dark days of the late '70s and '80s," said Crouch in a reference to the years when English football hooliganism was considered to be at its height.
"It is completely right that strong action is taken and that anyone involved in last night's trouble is banned for life," added Crouch, a qualified Football Association coach.
The police said 30 people were stopped from attending the game prior to the match between the two London sides. Chelsea supporter Paul Streeter said he and his eight-year-old daughter were pelted with coins while sitting in the disabled supporters' section of the ground.
"My daughter was hit with seven coins all over her body," he told BBC radio. "Other kids were hit, it was not just my daughter.
West Ham said they would request "severe banning orders"
A Chelsea spokesman said the Blues were "extremely disappointed" by the disturbances and the club condemned such behaviour.
West Ham manager Slaven Bilic also condemned the violence, which overshadowed a fine performance by his side.
"We are totally against it as a club," said the former Croatia defender, whose team will visit Manchester United in the quarter-finals.
"For those kind of things to happen, especially in England, is unacceptable."
Chelsea manager Antonio Conte added: "I don't like this type of situation. Above all in England, we are used to see the right atmosphere. This country is fantastic in this aspect."
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