Eight fire engines and around 60 firefighters were called to tackle the blaze yesterday, which involved trees and shrubbery near the railway tracks.
Crews brought the fire under control at around 10pm, but remained at the scene overnight to monitor for any flare-ups.
Urgent repairs are now being carried out, forcing the closure of all lines in and out of the station and causing major travel disruption.
Elizabeth line services remain suspended between Whitechapel and Ilford, while Greater Anglia has advised passengers not to travel on routes to, from or through Stratford until later today.
London Overground services are also affected, with cancellations, alterations and severe delays expected. Disruption is expected to continue throughout the day.
Footage shared on social media showed thick smoke billowing into the sky as flames tore through the vegetation close to the railway line.
Around 1,400 passengers had to be evacuated from nearby stopped trains which could not enter the station.
London Fire Brigade (LFB) confirmed that they received the first of around 30 calls at 6.54pm and that crews were mobilised from Plaistow, Poplar, Ilford, Bethnal Green and surrounding fire stations to the scene.
The public have been advised to avoid the area.
It is not yet clear whether the hot weather was responsible for the blaze.
LFB previously said that firefighters were assisting the British Transport Police to safely decant passengers from a number of trains that were stopped near the station.
National Rail said on their website: “A fire next to the track in the Stratford (London) area means all lines are closed.
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“Trains running through this station will be cancelled or revised. Until lines reopen and trains in the area are able to move again services will also be severely delayed.”
The Elizabeth line, Overground, and Greater Anglia services will be affected for the remainder of the day.
A number of London Underground services are also being disrupted by the blaze.
Only Central, Jubilee line and DLR trains are calling at Stratford.
There is no service between Highbury & Islington and Stratford, with severe delays are affecting on the rest of the line.
One passenger took to social media to say they were stranded on their way to a wedding.
They wrote: “I’m sat on a Greater Anglia to Norwich and we are stuck on the tracks!”
Station Commander Scott Thorpe, who is at the scene, said: “This fire was predominantly located within an area of grass and shrubbery that was surrounded on all sides by railway tracks. Crews also worked to extinguish other pockets of fire in around the station's sidings.
"The power to the railway tracks was isolated and the Brigade liaised closely with its multi-agency partners in order to resolve this incident safely.
"Firefighters worked hard to bring this fire under control as swiftly as possible; and we retained a presence through the night to ensure all areas had been fully extinguished."