Labour MP and London mayoral contender Diane Abbott has tabled an early day motion in the House of Commons calling on City Hall to reconsider the use of public funds for the Garden Bridge.
No other MPs have yet signed the EDM tabled by Ms Abbott.
The motion "urges the Government to make representations to TfL and the Mayor of London asking them to reconsider the project and consult the public and key stakeholders before proceeding with it".
The text of Ms Abbott's EDM also criticises the use of public money for a project "which will lead to the South Bank river walkway being narrowed [and] many trees and much green space ironically being sacrificed for a project which is labelled as green".
The EDM suggests that other parts of London have a more pressing need for a new river crossing.
Last month – during a live broadcast of BBC Radio 4's Any Questions? from Waterloo – Diane Abbott said that she would stop the Garden Bridge project if she becomes Mayor of London next year.