Mr Khan commissioned a report last year on overseas investment in London’s property market which found that although the number of entirely empty homes was very low overall, there was a greater number of empty homes in prime and expensive locations.
It was found that in Westminster’s top tax band H – where properties may be worth many millions of pounds – the empty homes levy would currently only generate £688 a year.
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In his letter, Mr Khan asked for boroughs to be able to increase the empty home council tax levy on high-value properties above the 50% of council tax currently allowed.
Mr Khan said: “The housing crisis is the biggest challenge facing our city today and I’ve been honest with Londoners from the start – we won’t turn things round overnight.
“This is going to be a marathon, not a sprint and we need to be able to take robust action to tackle it.
“In the midst of a housing crisis, just one home left unoccupied is one too many.
“That is why I will be working closely with boroughs like Westminster City Council to fight Londoners’ corner by calling for the government to allow boroughs to charge a higher council tax on empty properties at a rate that makes a difference.”