Also, the report doesn't tell us how many non-vacant homes there are in their survey area, so we have to guess. London reportedly has 3.59 million dwellings, so 25,000 vacant homes would only represent 0.7% of homes being vacant. Even if you use the higher 125,000 number, that's still only 3.5% of all homes. That's a fairly low vacancy rate, and about right for a city.
Even after the pandemic, housing officials report a 3.4% vacancy rate, which is the highest in eight years. https://lfpress.com/news/local-news/london-apartment-vacancy.... Before that, it was only at 1.8%. That's extremely low.
You can tax vacant homes, but in general, those taxes have a very small effect on housing prices. It's far, far more effective to allow people to build more housing, including luxury housing.
If the economy cannot consume all the products the suppliers produce you need to encourage consumption.
If you perfectly hit the balance (unlikely but in theory possible) then you need to do... nothing, neither savings nor consumption increases.
It depends on what your economy needs.
"Wealth investment leaves an estimated 125,000 homes in London without anyone living in them."
There are 268,385 empty homes in England according to the government (people get a tax break in most parts of England if they own a property that is unoccupied and unfurnished so its quite easy to track empty homes), and half of them are luxury houses in London.
I'm not saying that's definitely the case everywhere, but I am saying it's worth considering.