Twelve fire engines and around 80 firefighters were called to a flat fire on Wellington Way in Bow.
Half of a five-roomed flat on the 16th floor of the building was damaged by fire. Two people left the affected flat before the Brigade arrived.
Station Commander Keith McDermott, who was at the scene, said: "The fire is believed to have started in the bedroom of the flat and spread to the hallway.
"The Brigade's 999 Control Officers took 66 calls to the blaze and gave vital fire survival guidance to residents on how to stay safe before firefighters arrived. Crews wearing breathing apparatus rescued a man and a woman. One man was treated on scene by London Ambulance Service crews.
"We would like to remind people to never try to tackle a fire yourself. As soon as you become aware of a fire inside your property, get out, stay out, close the door behind you and call 999.”
The fire is believed to have been accidental and caused by the failure of a lithium-ion battery for an e-bike that had been on charge.
A London Fire Brigade spokesperson said: "Electric bikes and scooters are often stored and charged in escape routes in homes or communal areas so when a fire does occur, escape routes are blocked which immediately makes an already serious situation much more frightening for those involved so please do be mindful of where you're storing them.
"We have already issued a warning that many of the e-bike fires we are seeing involve batteries which have been sourced on the internet, which may not meet the correct safety standards.
“We know that lithium-ion batteries are susceptible to failure if incorrect chargers are used, so it’s important to always use the correct charger for the product and buy an official one from a reputable seller.
“Batteries can also pose a risk if they have been damaged, so try to ensure they are not getting knocked around while in use or while being carried as spares as this can increase the chance of damage to cells. You should also not expose them to extremes of temperature.
“You should always make sure you unplug your charger once it’s finished charging. Always follow manufacturers’ instructions when charging and we would advise not to leave it unattended or while people are asleep.”
The Brigade was called at 1046 and the fire was under control by 1142. Fire crews from Dowgate, East Greenwich, Dockhead, Stoke Newington, Euston and surrounding fire stations attended the scene.