The possible staff absence levels were reported by the Health Service Journal (HSJ) as the capital deals with the rapid spread of the Omicron variant of Covid-19.
The strain is now the dominant coronavirus variant in London, and the Mayor, Sadiq Khan, has said the surge in cases is “hugely concerning”.
Figures on Sunday showed cases of the variant in London had topped 10,000.
Mr Khan declared a major incident on Saturday, amid fears about staff absences due to the infection in vital public services including the NHS, fire service and police.
The HSJ said internal NHS monitoring figures seen by the journal showed that the number of healthcare staff in the capital absent due to Covid-19 had more than doubled in four days.
One in three of the workforce would be absent by New Year’s Eve if the growth rate continued, the journal reported.
Patricia Marquis, the Royal College of Nursing’s England director, said such a situation “would be catastrophic, there is no doubt about it”.
She told BBC Radio 4’s The World This Weekend: “The workforce is already short, the workforce is already exhausted – mentally and physically – so the prospect of that just must fill everybody on the frontline, and the public, with real concern, because the NHS just has to be able to cope with emergency and urgent care in order for the public to feel safe.”
She said staff were exhausted and the “prospect of not knowing what is happening just adds an extra layer of concern for people”.
She added: “Winter is difficult at the best of times.
“In the current situation it doesn’t look like there’s an end in sight and that makes the situation sometimes feel even more hopeless than it might actually be.”
Chris Hopson chief executive of NHS Providers, said pressure on London trusts, including hospitals, community mental health and ambulance trusts, had been “mounting rapidly” in the past week.
He told Times Radio: “The number of hospitalised Covid patients or patients who tested positive for Covid has gone up by 30% in a week, at a time when nationally it’s only gone up by 4%.
Figures from the UK Health Security Agency on Sunday showed that cases of the variant in London had risen by 2,937 from the previous day, to 10,092.
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