UK Health Security Agency data shows 561 people tested in the week to October 21 were found to be positive – a 5% decrease from 589 reported in the seven days to September 23.
The average rate of infection in Bassetlaw over the period stood at 474 cases per 100,000 – lower than 498 recorded a month earlier.
The highest number of cases recorded in the week to October 21 were among youngsters aged 10 to 14 (86), followed by teenagers aged 15 to 19 (50) and 50 to 54-year-olds (49).
Labour is calling on the Government to reintroduce some measures included in its "plan B" proposal, such as mandatory mask wearing, home working and vaccine passports for large events and nightclubs.
It comes as health leaders, including the British Medical Association and some Government advisers, have raised concerns about the increase in cases nationally.
Across the UK, 325,700 cases were reported in the week to October 21 – 38% more than the 235,700 recorded four weeks earlier.
However, the number of people who died within 28 days of a positive test result for Covid-19 showed a decrease over the same period, from 998 to 909.
In Bassetlaw, six deaths were recorded in the week to October 21, while there were none in the seven days to September 23.
Professor Peter Openshaw, a member of the New and Emerging Respiratory Virus Threats Advisory Group which advises the Government, said case numbers and death rates are currently “unacceptable”.
He said measures such as working from home and mask wearing are “so important” as part of efforts to control the spread of Covid.
Speaking in a personal capacity, Prof Openshaw, of Imperial College London, said: “We know that with public health measures the time to act is immediately. There’s no point in delaying.
“If you do delay then you need to take even more stringent actions later.
“We all really want a wonderful family Christmas where we can all get back together.”
He added people should start changing their behaviour, such as avoiding crowded places and public transport, without waiting for the Government’s instructions.
Health Secretary Sajid Javid has rejected calls to move to plan B, but said the Government would keep the situation under review.
Mr Javid added no “sensible health secretary” would want to predict what the situation will be like in the coming months.
He said: “We all want a fantastic Christmas and we can ensure that by getting out there and getting our vaccines.
“There are still some five million people out there that haven’t had a single dose of the vaccine.
“It’s getting darker, we can see it’s getting colder, we will spend more time indoors, and so we should think about hand hygiene, about getting tested regularly.”
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