The warning comes after figures showed UK Covid cases jumped by 32% in a week.
Dame Jenny told the BBC's Sunday Morning programme: "It doesn't look as though that wave has finished yet, so we would anticipate that hospital cases will rise."
She added: "For this particular wave we have some evidence there may be some slight reduction of the effectiveness of vaccines on variants, but they are still maintaining the majority of people, keeping them safe from severe disease and out of hospital."
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