Greenwich Council has issued a statement following the disorder in Blackheath Common near the funfair yesterday.
The Royal Borough of Greenwich said it is "appalled" by the disturbance which saw seven people arrested and a number of assaults on Tuesday afternoon.
The Council said it caused distress to people hoping to enjoy a fun day out with the family.
The funfair was set to reopen at 1pm today, but this has now been delayed.
Although it is hoped that the funfair will open as planned on Thursday afternoon, a spokesperson for the Council said this will be reviewed on Thursday morning.
Fair organisers are increasing security measures at the site in anticipation of reopening safely.
A Council spokesperson added that it "wants to make sure that community events like this continue to entertain residents".
The Council has asked parents to work with it by knowing where their children are as much as possible and encouraging them to look after themselves and each other.
The full Council statement said: "The Royal Borough of Greenwich is appalled by the disturbance at the funfair in Blackheath yesterday afternoon which caused distress to people hoping to enjoy a fun day out for all the family.
"We are working closely with the police and the funfair organisers to ensure the safety of everyone.
"The funfair will remain closed to the public for the rest of the day, with the decision reviewed on Thursday morning.
"Fair organisers are increasing security measures at the site in anticipation of reopening safely.
"The Council is proud to continue the long tradition of the funfair on Blackheath over Easter and we want to make sure that community events like this continue to entertain Royal Greenwich residents.
"With this in mind, we are asking all parents to work with us to keep our children safe.
"This means making sure you know where your children are as much as possible and encouraging them to look after themselves and each other.
"If anyone has any information or details about the disturbance yesterday, please contact the police by calling 101.
The Blackheath Bank Holiday funfair organisers said: "Notice to all our Customers
"Due to the anti-social behaviour that occurred in Greenwich Park and on Blackheath Common yesterday, the Royal Borough of Greenwich, has requested that the fair remains closed today.
"The Council and the Metropolitan Police acknowledge that the fair did not contribute to yesterday’s incident; they have congratulated the Showmen’s Guild on there swift and decisive actions in dealing with the situation.
"However they feel that until the Police can find resources to police the area, it would be best not to open today.
"We hope the fair will open as planned at 1:00 p.m. tomorrow, Thursday 14th April.
"Thank you for your support and hopefully we will have a fun-filled bank holiday weekend."
Officers were called to antisocial behaviour reports and a number of assaults in Greenwich Park at around 4.20pm on Tuesday.
A cordon was put in place to help disperse large crowds and a number of police resources were sent to the scene.
A stabbing had also been reported but after a search of the area no victim was found.
Police have now confirmed they are content that no stabbing took place.
Seven people were arrested on suspicion of possession of an offensive weapon and "related offences".
By around 6.15pm the area had been cleared.
A section 60 order was in place in the area until 7am today - allowing police to stop and search anyone in the area.
The disorder occured near to the scene of the Blackheath Bank Holiday Funfair which was forced to close early at around 6pm.
A Met Police spokesperson said: "Police were called at about 16:20hrs on Tuesday, 12 April following reports of antisocial behaviour and a number of assaults at Greenwich Park.
"A stabbing has also been reported; following a thorough search of the area no victim was found.
"Officers are therefore content that no stabbing took place.
"A number of police resources were sent to the scene and a cordon was put in place to help disperse the large number of people in attendance.
"By about 18:15hrs the area had been cleared.
"A section 60 was authorised and was in place until 07:00hrs on Wednesday, 13 April.
"Seven people have been arrested on suspicion of possession of an offensive weapon and related offences."
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