The council is consulting on a ban on the length of its borough boundary on the north of the river from before Hammersmith Bridge to near Imperial Wharf, a distance of over three miles.
A Public Space Protection Order (PSPO) would be brought in and police officers and the council’s enforcement officers would have the powers to issue fines following a warning.
A council consultation into the policy said: “Residents have reported safety concerns along the Thames Path due to e-scooters and e-bikes. Some residents report feeling unsafe due to the speed of these vehicles, concerns around the obstructions in public walkways, and collisions.
“We want pedestrians to feel safe when taking walks and travelling along the Thames Path.
“We are considering introducing a PSPO to prohibit the riding of e-scooters and e-bikes and other motorised vehicles along the Thames Path. We are also considering the prohibition of reckless riding of pedal cycles.”
It added: “If a person fails to comply with the requirements of the order following a warning from an authorised council or police officer, they will be issued with £100 Fixed Penalty Notice (FPN) and taken to court if the fine is not paid within the specified timeframe.”
The rules would not apply to mobility scooters or other mobility aids. The consultation, which can be viewed here, comes to a close on Sunday, January 29.
It comes amid rising concerns about e-scooter safety in London and the amount of police enforcement.
Most recent figures, covering the year to June 2022, showed 243 pedestrians were injured in collisions across Britain, including one fatality.
Including e-scooter riders, there were 1,437 casualties in collisions involving the devices, compared to 1,033 in the year ending June 2021. 12 people were killed.
Last month East London senior coroner Graeme Irvine warned fatalities from e-scooter crashes more than doubled after police changed policy to confiscate fewer of the devices.
Private e-scooters are banned on public land in the UK but are often used by people roads and pavements.
Rental e-scooters are the only way to legally ride one of the devices on public roads or in other public places within London.
Hammersmith and Fulham is among boroughs where e-scooter hire is available as part of trials.