Police have encouraged the public to attend Armed Forces Day events as normal after it was reported that the parade had been targeted by Islamic State.
The suicide blast at a parade in south London on Saturday was intended to strike soldiers from the unit of murdered Lee Rigby, according to The Sun.
The plot to explode a pressure cooker bomb — killing soldiers and bystanders on the route — failed after an IS leader in Syria unwittingly recruited an undercover investigator from the newspaper to carry it out.
It is claimed that a leading figure in IS, whom it named as Junaid Hussain.
Police have urged members of the public to attend Armed Forces Day events as normal
Hussain, originally from Birmingham, told the investigator: "It will be big. We will hit the kuffar (unbelievers) hard InshAllah. Hit their soldiers in their own land. InshAllah. Soldiers that served in Iraq and Afganistan will be present. Jump in the crowd and detonate the bomb.
"They think they can kill Muslims in Iraq and Afghanistan then come back to the UK and be safe. We'll hit them hard InshAllah."
The newspaper said the plot to bomb the parade in Merton was thwarted when it told police and security services about it.
The parade was targeted because it was closest to the barracks in Woolwich, south east London, where Fusilier Rigby, 25, was murdered by Islamist extremists in 2013, the newspaper said.
The attack was intended to strike soldiers from the unit of murdered drummer Lee Rigby
Fusiliers from his regiment, serving Gurkhas and war veterans will be among the 250 marchers, it added.
A Scotland Yard spokesman said: "The police, together with our security partners, remain alert to terrorist threats that may manifest here or where individuals overseas may seek to direct or inspire others to commit attacks in and against the UK.
"It is always helpful when journalists share with us information, as The Sun did in this case, that could indicate terrorist or criminal activity."
The spokesman cited the terrorist attacks in Tunisia, France and Kuwait on Friday as examples of the "global nature of terrorism and the threat level in the UK from international terrorism remains unchanged at severe".
The Islamic State has claimed responsibility for the Tunisia shootings that have left 38 dead, and the suicide bombing in Kuwait that killed 25.
The spokesman said the public should continue to attend the parade as planned: "While the UK threat level from international terrorism remains severe, we would like to reassure the public that we constantly review security plans for public events, taking into account specific intelligence and the wider threat.
"Our priority is the safety and security for all those attending or involved, the public are encouraged to continue with their plans to attend or take part in events as normal.
"We would also like to reiterate our long-standing advice to remain vigilant and alert."