NHS England's medical director, Stephen Powis, said health services are on "a war footing", with Covid-related staff absences more than doubling in a fortnight.
NHS England data shows 601 staff at Bedfordshire Hospitals NHS Foundation Trust were off sick on December 26 – the latest date for which data is available.
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There is no further breakdown between Bedford and Luton & Dunstable hospitals.
Of them, 326 (54 per cent) were off because they had Covid-19, or were self-isolating due to the virus.
This was a 61 per cent increase on a week before, when 203 Covid-related absences were recorded.
Across England, the number of NHS staff off work due to Covid increased from 18,800 on December 19, to 24,600 on Boxing Day – a 31 per cent rise.
Professor Powis said new nurses and reservists were being recruited to deal with pressures, as Nightingale hubs are being set-up across the country to tackle a surge in coronavirus patients.
He added: "We don’t yet know the full scale of rising omicron cases and how this will affect people needing NHS treatment, but having hit a 10-month high for the number of patients in hospital with Covid while wrestling with sharply increasing staff absences, we are doing everything possible to free up beds and get people home to their loved ones."
He added that keeping as many NHS staff as possible at work in the next few weeks would be essential.
People who receive negative lateral flow results on day six and day seven of their self-isolation period – with tests taken 24 hours apart – no longer have to stay indoors for a full 10 days.
But calls are growing on the Government to cut this further, after the US Government slashed the self-isolation period to five days for asymptomatic cases.
NHS Providers chief executive Chris Hopson said staff absences could pose a bigger challenge to the health service than patients needing treatment for the virus, with staff having to be redeployed to fill gaps.
The Government said while early evidence suggests the new coronavirus variant Omicron is less likely to cause serious illness than earlier waves, it stands ready to impose new measures in England if necessary.
England is the only country in the UK to have ruled out additional restrictions before the new year.