NHS Nightingale hospitals in some worst affected regions in the North of England are being asked to get ready to take patients.
Government advisers say admissions are rising, with more elderly people needing urgent treatment for Covid.
More people are now in hospital with Covid than before restrictions were announced in March.
England’s deputy chief medical officer said a “marked pick-up” in cases would lead to more deaths.
Prof Jonathan Van-Tam said: “Already, with the cases that we know about, we have baked in additional hospital admissions and sadly we also have baked in additional deaths that are now consequent upon infections that have already happened.”
He warned that coronavirus was spreading from younger age groups into the over 60s who are more vulnerable.
Cases are rising across most of England, but the North West is the worst affected.