No evidence has been found of a link between Westminster attacker Khalid Masood and so-called Islamic State or al-Qaeda, Metropolitan Police say.
The Met told BBC Panorama it was also "speculation" to suggest Masood had been radicalised while in prison.
Masood killed three people when he drove a car into pedestrians on Wednesday. He then fatally stabbed a police officer before being shot dead.
Police believe he drove up to 76mph as he crossed Westminster Bridge.
The attack took place within 82 seconds.
'Echo IS rhetoric'
The Islamic State group has previously said it was behind the attack.
But Deputy Assistant Commissioner Neil Basu said while Masood "clearly had an interest in Jihad", police had so far found no evidence of an association with the group or al-Qaeda, or that he had discussed his plan with others.
He said: "His methods appear to be based on low sophistication, low tech, low cost techniques copied from other attacks, and echo the rhetoric of IS leaders in terms of methodology and attacking police and civilians, but I have no evidence or information at this time that he discussed this with others."
Mr Basu said there was also no evidence Masood was radicalised in prison in 2003.
He said Masood had not been a subject of interest or part of the current domestic or international threat picture for either the security service or counter-terrorism policing.
There is also no evidence or intelligence that he was a subject of interest or a national security threat in security service or counter-terrorism police investigations connected with Luton or the long-banned al-Muhajiroun network.
He added: "I know when, where and how Masood committed his atrocities, but now I need to know why. Most importantly so do the victims and families."
Masood's victims were PC Keith Palmer - who was stabbed outside Parliament - Aysha Frade, who was in her 40s and worked at a London sixth-form college, US tourist Kurt Cochran, 54, and retired window cleaner Leslie Rhodes, 75, from south London.
Thirteen people are understood to remain in hospital.
It is understood the car Masood used was seen driving in the area around the bridge at some point before the attack.
It may have been on the day or before that, although it remains unclear what the purpose of this was.
On Saturday, the Metropolitan Police said they believed Masood acted alone but they were also "determined" to find out whether he had been inspired by terrorist propaganda.
However, Scotland Yard said it was possible they would "never understand why he did this".
It is understood Masood's phone connected with messaging app WhatsApp minutes before the attack, which police say started at 14:40 GMT.
An image of Masood's Whatsapp status shows that he was "last seen" on the messaging service at 14:37.
The revelations have prompted a debate about the responsibilities of messaging services.
Home Secretary Amber Rudd said encrypted messages must be accessible to intelligence services fighting terror, stressing there must be "no place for terrorists to hide".
She is holding talks with other EU ministers in Brussels to discuss ways of preventing further attacks and will later this week meet technology firms.
A WhatsApp spokeswoman said the company was "horrified at the attack" and was co-operating with the investigation.
- 14:40:08 - the car that Masood was driving over Westminster Bridge first mounted the pavement on the northbound side
- 14:40:38 - after continuing towards Bridge Street along both the footpath and road, Masood crashes into the perimeter fence of the Palace of Westminster
- 14:40:59 - the first 999 call was made to the Met police reporting the incident
- 14:41:30 - Masood left the vehicle and was shot by a police firearms officer inside the Palace of Westminster
Earlier, the family of the US tourist killed in the attack said he bore no ill will to anyone and spent his life "focusing on the positive".
Kurt Cochran's family said they had "felt the love of so many people" since his death.
Mr Cochran had been with his wife, Melissa, on the final day of a holiday in Europe to celebrate their 25th wedding anniversary - their first trip abroad. She suffered a broken leg and rib and a cut head.
Thirteen members of Mr Cochran's family attended a press conference at Scotland Yard to speak in public for the first time about the attack.
Mrs Cochran's brother, Clint Payne, said Mr Cochran "wouldn't bear ill feelings towards anyone and we can draw strength as a family from that".
He said: "His whole life was an example of focusing on the positive. Not pretending that negative things don't exist but not living our life in the negative - that's what we choose to do."
Meanwhile, Foreign Office minister Tobias Ellwood, who was hailed a "hero" for giving first aid to PC Keith Palmer, said he was "heartbroken" he could not do more to save the policeman's life.
Mr Ellwood, a Conservative MP and former Army officer, performed mouth-to-mouth resuscitation on PC Palmer in New Palace Yard, Westminster.
He tweeted that he had been "deeply humbled and overwhelmed" by the messages of support he had received since the attack.
Officers investigating the attacks are holding two people from Birmingham on suspicion of preparing terrorist acts. Nine people have so far been released without charge, while a 32-year-old woman arrested in Manchester remains on police bail until late March.
The Metropolitan Police said Masood, 52, who had previous criminal convictions but none for terrorism, had used a number of aliases.
At birth, he was registered in Dartford, Kent, as Adrian Elms, but later took his stepfather's name becoming Adrian Ajao in childhood.
In the early 2000s, he was convicted of causing grievous bodily harm after slashing a man across the face with a knife in a pub.
A tribute to the victims of the attacks was made at Wembley Stadium on Sunday evening when fans and players at England's World Cup qualifier against Lithuania observed a minute's silence before kick-off.
Four wreaths were laid on the pitch by Metropolitan Police Acting Commissioner Craig Mackey, London Mayor Sadiq Khan, FA chairman Greg Clarke and Culture Secretary Karen Bradley.