Just on the route, I need to see it in person but it looks like the bus stop before Wandsworth Bridge may be the problem. It’s the difference between this being a route that someone would take their children on, or not.
It could easily be resolved by putting a contraflow cycle lane on Jews Row. If the route had been the responsibility of one authority, that’s a decision that could have taken to remove any conflict elsewhere.
But because it’s a private estate that hasn’t happened, they’re not concerned with any access through or beyond their own boundary unless it’s enforced.