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Dartford's council leader says they are being "very cautious" and constantly monitoring Covid-19 data after a new variant emerged in the town.
Nearly 100 local authorities across the UK have seen five or more cases of B.1.617.2, the strain first detected in India.
Dartford has reported three cases according to data up to May 14 released by Public Health England, while alternative figures by the Wellcome Sanger Institute have the number of cases even higher.
However, overall cases of Covid-19 in the town had stayed roughly the same and rates of this new strain fell well below the numbers seen in the north west of the country and parts of London where it has become dominant in certain areas.
This includes Bolton – which has recorded more than 400 Covid cases per 100,000 people – and is one of eight areas to have been urged to only travel local.
A total of 97 local authorities with a combined population of more than 20 million have seen five or more cases of the emerging Indian strain.
This is compared to 36 council areas covering more than half that number of people just two weeks ago.
The rise in the so-called Indian variant, which is believed to be more transmissible, has caused alarm with the Prime Minister previously warning aspects of it could delay the final lockdown lifting on June 21.
Leader of Dartford council Jeremy Kite said spread of the new strain was "obviously a concern" but one that needed to be "put into perspective".
He said: "We are constantly monitoring the new data and any rise will be a concern but it is very clear we are dealing with levels that are significantly lower than at the peak. Of course we are concerned but we are concerned with it being a small figure."
The Tory councillor went on to explain new cases of the variant were a worry but the town's population of around 108,000 "put it into perspective".
"Of course we are concerned but we are concerned with it being a small figure."
Nevertheless, he said they were being "very cautious" and urged residents to "be vigilant", take precautions and to continue to get vaccinated when asked.
The variant, first detected in India, includes a number of different mutations. Public Health has identified thousands of cases of this variant in the UK and says all appropriate public health interventions will be undertaken, including enhanced contact tracing.
Scientists researching the variant believe vaccines being rolled out across the UK are "effective" against the strain.
The take-up of vaccines is seen as crucial to a returning to "normal life" and Cllr Kite has continued to urge residents to get on board.
"Our vaccine figures are good but they are not the best and we need to sort that," he said.
Elsewhere, council leaders across the country were reported to be angry with central government over changes made to the guidance for those in Indian variant hotspots and travel guidelines which they claimed had been "sneaked in" without consultation.
But Cllr Kite believes the guidance continues to be clear and said the people of Dartford will continue to use their "common sense" as they have done over the last 18 months.
"I don't think there is a lot of confusion," he said. "The people I speak to say 'I'm not going abroad'.
"I think Britain has changed in the last 18 months and people can't just look to the government for every bit of advice."
He said: "I think most people are understanding they have to be extremely careful", adding "it is about taking sensible steps".
"At the end of the day most people take the view of a little more sacrifice now."