The Metropolitan Police have released the route of a delivery lorry to which they believe Daniel Khalife strapped himself as part of his escape from prison.
More than 150 officers and staff have been working around the clock to try to apprehend Khalife, 21, the force said.
The police said a nationwide alert has been issued for the former soldier, leading to increased security at ports and borders.
There have not been any confirmed sightings of him.
The force said Khalife was declared missing at 7.50am on Wednesday and they were notified at 8.15am, when they took immediate action to track down the delivery lorry that had left the prison.
The Met Police published the following route taken by the lorry:
The lorry left HMP Wandsworth at 7.32am on Wednesday, taking a right turn out of the gates on to Heathfield Road.
It then turned left on to Magdalen Road.
The lorry then turned left on to Trinity Road (A214), up to the Wandsworth roundabout, taking the first exit on to Swandon Way (A217).
It then turned left on to Old York Road, past Wandsworth Town train station, then left on to Fairfield Street.
It turned right on to Wandsworth High Street (A3), staying straight ahead on to West Hill and then on to Upper Richmond Road (A205), where it was stopped by police near the junction with Carlton Drive at 8.37am.
The lorry had turned around by the time police stopped it and had been returning to Wandsworth prison because the driver had been phoned by Bidfood, the company which owns it.
The company has been “co-operating fully with the inquiry”, police said.
Officers spoke to the driver and then carried out a thorough search of the lorry.
During the search they discovered strapping on the underside of the vehicle, which they believe Khalife used as part of his escape.
A Bidfood spokesman said: “Yesterday morning we were made aware of a security incident involving one of our vehicles, whilst out on delivery.
“We can confirm that our driver fully co-operated with the police on this matter before returning back to the depot. We will continue to assist the authorities in their ongoing investigation.”