Darent Valley Hospital in Dartford said it had imposed mask rules and tighter visiting arrangements as cases surged.
Meanwhile, East Sussex Healthcare NHS Trust said it had also “instituted voluntary mask-wearing by patients, visitors and staff in our gateway areas”, which included emergency departments and assessment units, as well as areas where there were respiratory illnesses.
“Not everyone is able to wear a mask, but doing so can reduce the spread of respiratory conditions between patients and to our staff, so we appreciate everything which our patients and communities can do to help”, the trust added.
“While masks will not entirely eliminate the risks of transmission of flu and respiratory viruses, they do reduce their spread and provide a degree of protection.”
It can be enhanced by getting your flu vaccination and washing your hands, it added.
NHS England said there were enough flu patients nationally to fill more than three hospital trusts.
Health service chiefs said the total had already increased sharply since the week covered by the data, up to Sunday, with no peak in sight.
Projections suggested there could be between 5,000 and 8,000 hospital cases by the end of the second week in December. The highest ever recorded was 5,400.