The Mayor echoed calls from former Health Secretary Jeremy Hunt for a rapid acceleration in how quickly results are available to people being checked for the virus.
Mr Khan said a comprehensive “test-trace-isolate” system was essential to prevent a second wave of infections.
The capital has been the worst hit area in the country, with 5,697 deaths declared by NHS England last night – though the true toll including deaths in the community and at home will be much higher.
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Mr Khan said the capital’s greater levels of ethnic diversity and poverty – both key factors in covid mortality - made rapid testing crucial.
At present, tests are not freely available to all Londoners. Government guidance is for those who qualify to apply for a test in the first three days of experiencing symptoms, with it potentially taking one or two days to arrange. It can then take more than three days to get the result.
The Mayor believes testing must be available to everyone who needs it on the first day they develop symptoms and the results should be provided within 24-48 hours, with contact tracing to immediately follow in order to prevent the spread of the virus.
He said: “It was a mistake for the Government to abandon this approach in early March and it must now make up lost ground so our city can start to re-open safely.
“We have a small window of opportunity to stop the virus spreading further, so it’s vital the Government acts now.
“We have seen the important role that these systems have played in saving lives and restoring public confidence in countries like Germany, Australia, New Zealand, South Korea and Singapore, and we’re ready to work with Government to ensure we have a system that meets London’s unique needs.
“It’s vital that this is in place before there is any further lifting of the lockdown so we can avoid a disastrous second wave of the virus that could overwhelm our NHS and result in more tragic deaths.”
Mr Hunt, chairman of the Commons health select committee, said it was taking "much too long" for Covid-19 tests results to be processed.
He told the Today programme: "If you call up because you have got Covid symptoms, you really need test results back in 48 hours. That's really got to happen very, very fast, otherwise there's no point."