While it is very unlikely that Alex Challoner will get the Tory nomination for Mayor let alone win the election, he has raised an interesting point about Hammersmith Bridge. That is that the problem isn't an engineering one but an administrative one. The bridge isn't reopening not because of the cost, or the challenges of restoring it but because of the complexities of ownership and blurred responsibilities.
If you could simplify these matters then the path to full restoration would be much clearer. TfL is the obvious home for the bridge, with a supportive government, the cost wouldn't be a huge part of its budget. The Mayor has hinted that this is the way he would like things to progress so a consensus seems to be developing.