Professor Derek Ward, Lincolnshire County Council’s director for public health, warned that if numbers did not go down nationally, then government may consider tightening lockdown rules even further.
East Lindsey’s latest 7-day figures up to November 14 show 787 new cases — an infection rate of 555.3.
The England average is 274.3 per 100,000 population.
Professor Ward told BBC Radio Lincolnshire: “I think we should be concerned but not alarmed.
“What we have seen right the way through is definitely an increase across the county, but specifically East Lindsey.”
However, he added: “Over the past few days [our own figures] have seen a change, in that they have flattened out and started to come down, but it’s early days.”
He said there was particular concern for the over 60s in the district and specifically repeated warnings against travelling where possible.
It comes as people continue to travel into North East Lincolnshire for work and shopping.
“The challenge will be in the next week, if we don’t see numbers come down, there’s definitely going to be some aspect of delay,” said Professor Ward.
“Government will consider tightening lockdown if we don’t see figures go down.”
Here are the latest government figures for the seven day period to November 14, including case numbers and infection rates per 100,000 population from highest to lowest:
• East Lindsey, 787 cases, 555.3
• Boston, 330 cases, 470.3
• Lincoln, 448, 451.2
• North Kesteven, 362, 309.6
• West Lindsey, 264, 276
• South Kesteven, 331, 232.4
• South Holland, 215, 226.3