London's mayor dismissed fears a permanent monument might become a magnet for extremists.
Lyn Rigby speaks exclusively to Good Morning Britain about her ongoing grief and described why she will never forgive her son's murderers.
In her only television interview since the verdict, she told ITV News that she begs forgiveness from Lee Rigby's family.
A mother and daughter who stopped their car and got out to try and help Lee Rigby have said they are still traumatised by what they saw that day in May.
They said despite being in jail it's unfair that Michael Adebolajo will see his children grow up, when Lee Rigby will never see his son again.
Juliet Bremner reports.
The Metropolitan Police's Assistant Commissioner Cressida Dick, who is responsible for counter-terrorism, said her thoughts are with Fusilier Lee Rigby's family after his killers were found guilty of murder.
She told ITV News UK Editor Lucy Manning it was "an appalling act” on a “completely innocent young man with no chance to defend himself in broad daylight on a busy London street.”
When asked if a similar attack could happen again, she said: "It's our job to do everything we can to try to stop such attacks and we do have, I think, a very good record in this country.”
However Ms Dick said: "We cannot reduce the risk of something like this happening to absolute zero. We'll do everything in our power to do so."
Lewisham Islamic Centre has distanced itself from any association with Michael Adebolajo, 29, and Michael Adebowale, 22, who were found guilty at the Old Bailey today over the murder of Fusilier Lee Rigby.
The centre said in a statement: "We can categorically confirm that the individuals were not associated in any way, shape or form with the Lewisham Islamic Centre and/or its staff".
Muslim Council of Britain secretary general Farooq Murad said the killing of soldier Lee Rigby was "a dishonourable act," adding: "No cause justifies cold-blooded murder."
Mr Murad said: "The murder of Drummer Lee Rigby was truly a barbaric act.
"Muslim communities then, as now, were united in their condemnation of this crime."
Mayor of London Boris Johnson has condemned the murder of Lee Rigby as barbaric, heinous and completely unjustifiable after Michael Adebolajo and Michael Adebowale were found guilty of the Fusilier's murder.
"The murder of Lee Rigby was barbaric, heinous and completely unjustifiable," the Mayor said.
"Fusilier Rigby was a dedicated and professional young man whose life was taken in the most casual, brazen and horrific fashion, in broad daylight on the streets of London.
"This is a city that prides itself on tolerance, diversity and openness, values that stand in marked contrast to the actions of Lee's killers.
"Lee's courage, and that of those members of the public who sought to protect him, as well as the extraordinary bravery of the police officers involved are what we should remember today."
David Cameron said the murder of Fusilier Lee Rigby "shows that we have to redouble our efforts to confront the poisonous narrative of extremism and violence that lay behind this and make sure we do everything to beat it in our country."
Speaking to reporters in Brussels, the Prime Minister said: "The whole country was completely shocked by the murder of Lee Rigby and the whole country united in condemnation of what happened."
"I'm sure everyone will welcome these verdicts today," he added.
Colonel Jim Taylor, of 2nd Battalion, Royal Regiment of Fusiliers, had taken command just three weeks before Lee Rigby's death.
The first time he addressed his soldiers was to deliver the news of their comrade's murder.
He told ITV News correspondent Geraint Vincent that it was a "tragic set of circumstances and a brutal way to die."
He also said the Fusiliers "have become very resilient in their outlook in the way that they have dealt with deaths on operations...and to the tragic events - terrorist related - of Lee's death.
"It is a bitter experience for everyone to go through, regardless of how it happens," he added.