Clinton Henry, 28, was spotted by police officers who saw him travelling at speed on Molesworth Street, also in Lewisham, about 12.30am on April 11.
The electric scooter pulled away from traffic lights and accelerated almost instantly to around 30mph.
When he was stopped by police, Henry admitted that he had no licence or insurance and said he did not know they were needed for e-scooters.
After initially refusing, he eventually gave a breathalyser test which found he contained 77mcg of alcohol per 100ml of breath. The legal limit is 35mcg.
As well as being banned from driving for 17 months, he was fined £170 and ordered to pay £119 in costs and victim surcharge.
The vehicle – which was found to have no lights on and had a seat fitted – was seized by police.
Sergeant Steve Wilson, from the Roads and Transport Policing Command, said: “E-scooters remain illegal on London’s roads and pavements but we know there are still too many people failing to comply with the law.
“This case should serve as a reminder that an e-scooter is a motor vehicle, just like a car. If you are caught with one on a road or pavement, it could impact on your regular driving licence and lead to a fine of £300 and six penalty points.”