Fifty officers worked through the night stopping passers-by on both sides of the Thames at Hammersmith and on neighbouring west London bridges, in a bid to find witnesses who saw anything suspicious.
More than 24 hours after the explosion, no group has admitted planting the bomb, amid speculation that it was the work of dissident Irish republicans.
Security was being stepped up as police last night confirmed that the device comprised between 1kg and 2kg of high explosive, and was fully detonated.
Anti-terrorist officers supported by uniform officers stopped members of the public on neighbouring west London road bridges in Chiswick and Putney from about 1am today.
"We are speaking to motorists and passers-by who may have been in the area during that time period the previous night," said a Scotland Yard spokeswoman.
"We will be asking if they saw anyone acting suspiciously near the bridge or in a car before the explosion."
Deputy assistant commissioner Alan Fry, the head of Scotland Yard's anti-terrorist branch, urged people to be vigilant in the wake of the attack. "I am asking people that if they see a suspect package to contact us immediately on 999."
He added there would be more high visibility policing on London's streets in the wake of the bomb and said measures would be taken to reassure the public.
"I can tell you police had no prior notice - no threatening calls or anybody claiming responsibility."
Asked if there was a possible link with Irish terrorists he said: "I am not going to speculate but clearly they would be a line of inquiry."
The bomb went off without warning at around 4.30am yesterday, causing traffic chaos. The device, attached to a girder on the bridge, caused structural damage but no injuries. Residents living nearby described how windows in their homes were blown out by the force of the blast. The bridge might be closed to pedestrians and traffic for a number of weeks while engineers assess the damage and ensure the structure is safe.
The attack triggered a number of hoax calls including warnings a device had been planted in the Dartford Tunnel in Kent, causing it to be closed for 35 minutes.
Hammersmith bridge has been targeted twice before by terrorists, the last time in 1996 when the most-powerful Semtex bomb ever used by the IRA on the mainland failed to go off.
Ulster Unionist deputy leader John Taylor said dissident republicans trying to destabilise the peace process could have been behind the blast.
"If it's terrorist-linked I would expect it to be the breakaway groups within the republican movement, something like the Real IRA or the Continuity IRA," he said.
"Clearly, their objective now is to upset the Provisional IRA programme of putting arms out of use. It must always be remembered there are minority republican terrorist groups still on the ground, still potentially active."
Terrorism expert David George agreed that the attack was most probably the work of the Real/Continuity IRA, which broke from the Provisionals three years ago.
The bomb would have been planted by a small cell of activists, so-called "lilywhites" with no link to republican activities, who probably travelled from Northern Ireland, said Mr George, a lecturer in terrorism at Newcastle University.
If dissident republicans were involved, then this would be the first time they have launched an attack in mainland Britain.
