Hammersmith Bridge is now completely closed: this includes the riverside paths beneath the bridge. The 133-year-old structure is showing cracks in its cast iron, and these cracks have widened in recent weeks. For this reason, the route of the London Summits Walk (section 8) has been diverted via Putney Bridge, adding a little over 2km to the route.
I have mapped the route in the opposite direction: these map sections form the Capital C route.
These map sections (for both the London Summits Walk and the Capital C) are now made public on the OSMaps site.
London Summits Walk, Capital C, and Hammersmith Bridge
Lwalks.London 
Three months on, and no real progress on this. I have come to the conclusion that the best answer would be to build a new bridge. One of the heraldic bits could be relocated as a monument to Bazalgette’s work, but just look at the new Pooley Bridge (https://www.theguardian.com/artanddesign/2020/nov/22/pooley-bridge-reunites-the-lake-district): something as graceful as that would be a real improvement.
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