Heathrow says it has been overtaken as Europe's busiest airport for the first time by Paris Charles de Gaulle because of a slump in demand for air travel.
Heathrow said its passenger numbers were 84% down in the three months to September as the pandemic continued to ravage its business.
It expects just 22.6 million passengers next year, a quarter of 2019 levels.
Boss John Holland Kaye said Britain had been too slow to embrace passenger testing and was "falling behind".
He said Paris Charles De Gaulle and other rivals such as Amsterdam Schiphol had reopened faster because they had implemented testing regimes.
"Already in France and Germany, even Canada and Ireland have moved to testing and this is the way to make sure we can protect jobs in the UK as well as protecting people from coronavirus," Mr Holland Kaye told the BBC.
"The government really need to get on and make this happen before the beginning of December if we are going to save people's jobs."
This would reduce the amount of time arrivals from higher risk destinations had to spend in quarantine from 14 days - seen as a big deterrent to travel - to a week.
But Mr Holland Kaye told the BBC the industry still needed a "commitment" it would happen.
He added that the only way to really revive air travel was to bring in widespread pre-departure testing that met internationally agreed standards.
The airport has already begun offering such testing, but only for passengers travelling to destinations that require it.
He urged the UK government to speed up talks with the US over creating a "pilot air bridge" for such as scheme.
"That is the best way to make sure we are no longer importing Covid and also that people can travel with confidence."
Heathrow, which is already cutting 500 jobs, said its losses had widened to £1.5bn in the first nine months of the year.
But it said its finances were solid and it had reserves to tide it over until 2023.
The air travel industry has been hit hard by coronavirus, with airlines such as British Airways and Easyjet slashing thousands of jobs.
The International Air Transport Association, which represents 290 airlines, estimates that air traffic will not return to pre-pandemic levels until at least 2024.
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