James Furlong, a teacher, is the first victim identified
Second victim named by family in US as Joe Ritchie-Bennett
The third person killed has been named as David Wails
A minute's silence was held in the town at 10:00 BST
Khairi Saadallah, a 25-year-old Libyan national, is in custody
It is believed to be an isolated incident and police are not looking for anyone else
The attacks happened in Forbury Gardens in the town centre
Three people died following the attack and three more were treated for injuries
Police urge people not to share footage of the attack on social media
The prime minister said he was "appalled and sickened" by the attacks in Reading last night.
He said: "I don’t want to preempt the work of the police and their investigation into what happened in this case.
"But if there are changes that need to be made to our legal system to stop such events happening again we will not hesitate to take that action."
The UK prime minister says that if there are lessons to learn after the terror attack the government will learn them.
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Anthony Stansfeld, police and crime commissioner for the Thames Valley, said he was "deeply saddened to hear about the shocking events which took place last night".
He said: "Obviously this is an extremely upsetting event and my sincere condolences go out to the families of the victims and all those who have been affected.
“I would urge anyone with footage or information on the event to contact the police by calling 101 and quoting reference number 1159 20/6.
"I would like to thank the police officers who responded so quickly to this incident in order to protect the public."
The suspect was detained by unarmed officers, the Metropolitan Police's assistant commissioner Neil Basu said.
He praised the actions of Thames Valley Police, as well as those who gave emergency first aid to the victims.
Image source, PA MediaA 25-year-old man from Reading has been arrested on suspicion of murder and remains in custody.
Mr Basu said although "motivation for attack is far from certain" it was not associated with a Black Lives Matter protest which had finished "hours" before the attack.
The head of counter-terrorism policing gives an update following stabbings in Reading, which have been declared a terrorist incident.
Read MoreAssistant commissioner at Metropolitan Police, Neil Basu, said 41 witnesses had come forward following the attack.
In a statement at New Scotland Yard, he said officers were not looking for anyone else.
He described the stabbings as an "atrocity" and sent his "deepest sympathies" to the relatives of the three people who have died and those who have been injured.
Three people have died and three others have been injured in a series of stabbings in a park in Reading yesterday evening.
Here's what we also know:
Royal Berkshire Hospital in Reading has confirmed there were three casualties following the attack at Forbury Gardens.
Image source, David HowardTwo were treated at hospital.
One has been discharged, while the second remains an inpatient in observation, but their injuries are not life-threatening, a spokesman confirmed.
Flowers have been left in tribute to victims at a police cordon near the scene of the stabbings.
Image source, PA MediaOne reads: "There are no words that anyone can say to express how horrible and senseless this was.
"Our prayers are with all the victims and their families and friends.
"Reading stands united."
Another card said: "Reading weeps."
Prime Minister Boris Johnson has been briefed by security officials this morning over the attack at Forbury Gardens.
One of two people being treated at Reading Hospital has been discharged.
Officers from Counter Terrorism Policing South East have taken over the investigation, external.
Chief Constable John Campbell, from Thames Valley Police, said: “I am deeply saddened by the events of last night.
“This was a truly tragic incident and the thoughts of Thames Valley Police are with all those who have been affected.
“Incidents of this nature are very rare, though I know that will be of little comfort to those involved and understand the concern that this incident will have caused amongst our local community.
“We will be working closely with our partners over the coming days and weeks to support the Reading community during this time, as well as with CTPSE as they progress their investigation."
Three people were killed and three more were seriously injured in the attack at at Forbury Gardens at about 19:00 BST on Saturday.
A 25-year-old man from Reading was arrested on suspicion of murder after being detained at the scene.
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All Reading town centre buses are now only departing from St Marys Butts and Cheapside.
Many roads remain cordoned off with police tape.
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Counter Terrorism Policing can now confirm that the stabbing incident that happened in Reading last night, has now been declared a terrorist incident.
Free help is being offered to victims or witnesses of Sunday's attack in Forbury Gardens.
Supt Stan Gilmour, head of violence reduction unit at Thames Valley Police, has urged people who have been affected to make a referral to Victims First.
It offers "free emotional and practical support for victims and witnesses of crime", he said.
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Linda Serck
BBC South
The whole town centre area remains cordoned off, apart from Broad Street and King's Road.
The cordon is adding to the already eerily quiet streets due to the coronavirus lockdown.
In a statement Reading Borough Council, external said it was "shocked and appalled" at yesterday's attack at Forbury Gardens.
It said: "The Council’s thoughts and prayers are with the families of the three people who lost their lives, and for those who remain seriously injured.
"Along with residents of the town, we would also like to express our appreciation for the incredible response of colleagues in the emergency services who acted so swiftly yesterday evening to prevent further harm.
"As a mark of respect, the Council’s flag will be flying at half-mast today."
Alice Penney said she was "mortified" by the news
Residents and workers have reacted with shock at last night's news.
Alice Penney, who moved to Reading from Kent a year ago said she escaped out of Reading last night to a friend's house after she heard about the stabbings.
"I was absolutely mortified. I had been at the protest a few hours earlier when I heard the news. It was something I couldn't process.
"I feel like we cheated death. It's a safe place, normally. It's very confusing."