This isn’t a new idea: Sustrans last tried to promote the bridge around 2008.
Quoting from Brockley Central:
“A £65 million project to build a bridge for pedestrians and cyclists between Rotherhithe and Canary Wharf had been developed by Sustrans (the national cycling charity) and had been subject to a feasibility study by TfL, which concluded that the ideal location was between Durand’s Wharf, a park on the Southwark bank, and Westferry Road. The planned lift bridge would have been able to raise itself to varying heights, depending on the nature of the craft passing underneath and would have linked to public transport networks on either side of the river.”
This initiative failed when the Mayor of London and TfL withdrew support.