The Garden Bridge project alone swallowed tens of millions and remained completely unbuilt. That money could have been better spent elsewhere with greater results.
Yes it's true that the rest of the UK could benefit from more investment and that MIGHT make otherwise economically defunct areas slightly less economically defunct. Keyword might. London is a "will", not a might.
If you look at the geography of London it makes for a good port area for bringing goods to and from continental Europe, but it no longer does that like it used to. In the past it was highly dependent on coal from Yorkshire, South Wales etc and materials from elsewhere whether wool or metals. In the 1980s, the London stock market was bankrolled by North Sea oil, mostly in northern English and Scottish waters. Nowadays, London's chief thing is the finance industry and stock market, but that is not location dependent at all, and very easily transferred somewhere else which puts London in a more unsafe position than it realises. Like most major cities, it consumes a great deal of energy and gets its water from elsewhere (and some recycling).