LFB said fire damaged most of the first floor of the house and destroyed the loft and that the e-bike had been bought from an online marketplace.
One male fell from the roof and suffered serious injuries, while a woman slipped but was caught by a firefighter, and later treated for smoke inhalation.
LFB deputy assistant commissioner Richard Field described the fire as “devastating” and said it was “fortunate that no lives have been lost”.
He added: “We’ve seen around 160 e-bike and e-scooter fires in London this year and this incident highlights the dangers e-bikes and e-scooters can pose.
“E-bikes are one of London’s fastest-growing fire risks, with a fire on average once every other day.
“If you’re planning on buying an e-bike or e-scooter for yourself or a loved one for Christmas and you see an offer online that seems too good to be true, it probably is.”