Areas may struggle to staff NHS Nightingale hospitals should they be required during a second wave, a director of public health said.
Victoria Eaton, of Leeds City Council, described the potential of getting sufficient numbers as "incredibly challenging".
Nightingales in Manchester, Sunderland and Harrogate are being asked to be put on standby once again.
They were set up in the spring in case the NHS became overwhelmed.
On Monday, government advisers said hospitals had not reached capacity but the NHS may have to use some of the Nightingales if demand continues to rise.
Ms Eaton said: "The buildings are there, the issue is how we get the staffing into the Nightingales because, in spring, the workforce plan was for people who were stood down from other services to go to staff the Nightingales.
"So I think there is a real challenge around how to get enough NHS staff to make those sites work. It's incredibly challenging this time round."
In Leeds, Ms Eaton said hospitals wanted to clear their long list of delayed treatments and procedures.
"We've got a huge backlog now of people who desperately need surgery and treatment for their conditions, which colleagues in the NHS are absolutely committed to continue with, and therefore it gives them very little wriggle room within the hospital to accommodate all of those cases plus the new Covid ones that are now coming in," she said.
Liverpool University Hospitals NHS Foundation Trust chief executive Steve Warburton told staff in a memo on Monday that it had reached a "critical point".
He said the trust was scaling back planned procedures, adding it was "taking a phased approach to reducing our elective programme, while exploring options with other providers to maintain some of this work in alternative locations".
Professor Stephen Powis, NHS England's medical director, said hospitals in the North West and North East had witnessed a seven-fold increase in Covid patients in their intensive care units.
"If infections continue to rise, in just four more weeks they could be treating more patients than they were during the peak of the first wave," he said.
The government announced 17,234 confirmed cases on Tuesday, with 143 new deaths - the highest daily figure since 10 June.
However the BBC's Head of Statistics Robert Cuffe says this number is probably due to the weekend lag in reporting deaths.