British police said Monday they had found no link between the man behind last week's terror attack outside the British parliament and the Islamic State group, which had claimed him as one of its "soldiers".

The statement came as 52-year-old Muslim convert Khalid Masood's mother spoke out for the first time, saying she was "deeply shocked, saddened and numbed, and relatives of the US victim voiced their grief.

"Whilst I have found no evidence of an association with IS or AQ (Al-Qaeda), there is clearly an interest in Jihad," Neil Basu, deputy assistant police commissioner, said in a statement.

Masood was shot dead after ploughing through a crowd of pedestrians and fatally stabbing a policeman just inside the gates of the British parliament in a frenzied attack lasting just 82 seconds on Wednesday.

Four people were killed and dozens more injured.

Basu said Masood's low-tech methods appeared to be "copied from other attacks and echo the rhetoric of IS leaders in terms of methodology and attacking police and civilians but at this stage I have no evidence he discussed this with others".

He also said there was "no evidence that Masood, who was born as Adrian Elms, was radicalised in prison in 2003" as suggested in some media reports.

Basu said he changed his name to Masood in 2005.

Masood served two stints in prison for a knife attack in 2000 and again for knife possession in 2003.

"His last criminal offence was in 2003 and he was not a current subject of interest or part of the current domestic or international threat picture," Basu said.

The police commander said Masood's communications on the day of the attack were "a main line of inquiry" and he asked for anyone who had heard from him to come forward so as to establish "his state of mind".

The government has confirmed that Masood used the WhatsApp messaging service shortly before the attack, saying it was crucial that the security services be allowed to access the heavily encrypted app.

Twelve people have been arrested since the attack and two men remain in custody after nine were released without charge and one woman was let out on bail.

- 'Do not condone' -

Masood's mother Janet Ajao also on Monday released a statement saying: "Since discovering that it was my son that was responsible I have shed many tears for the people caught up in this horrendous incident".

"I do not condone his actions nor support the beliefs he held that led to him committing this atrocity".

The family of US tourist Kurt Cochran, who was one of the victims of the attack, spoke on Monday of a "humbling and difficult experience".

Cochran and his wife Melissa were in London to celebrate their 25th wedding anniversary -- their frist trip out of the United States.

She is still recovering from a broken leg, a broken rib and a cut to the head sustained in the attack.

In the first public statement by a victim's family since the attack, her brother Kurt Payne thanked the emergency services and members of the public for "the outpouring of love and generosity".

"The most difficult part of all of this is that Kurt is no longer with us, and we miss him terribly," he said.

"He was an amazing individual who loved everyone and tried to make the world a better place."

US President Donald Trump announced Cochran's death last Thursday, calling him "a great American" in a tweet. afp