Eastbourne could be in Tier 4 until at least March.
On Saturday, when the capital was placed under tier 4, the prime minister said the lockdown would be reviewed after two weeks.
However, Matt Hancock suggested the measures could be in place for much longer.
The Health Secretary said the new measures could be in place for the “next couple of months” due to the “highly concentrated” nature of the mutant strain.
The new mutant strain is more transmissible and responsible for a significant rise in the number of cases reported across all areas of Sussex.