Richmond Park’s MP has met with the Parliamentary Under Secretary of State for Transport, Lord Davies.
Sarah Olney wants pedicabs introduced so those who struggle to walk over the bridge can still access it.
The Grade II listed structure has been closed to motor vehicles since April 2019 following safety fears.
A similar trial scheme run by the Barnes Community Association in 2021 saw over 9,100 people carried across the river over 6 months.
Ms Olney says Lord Davies has expressed a willingness to explore the proposal of passing the Pedicabs (London) Bill into law.