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Folkestone and Ashford are on a list of 20 towns identified as 'areas of concern' for further coronavirus outbreaks.
The Government list was circulated to local health chiefs last week and is expected to be officially released within days.
The data could be used to enforce more local lockdowns like the one implemented in Leicester, where schools were closed and pubs and restaurants ordered to shut.
Leicester remains top of the list with 5.7% of individuals who underwent a test found to have the virus. Kirklees, in West Yorkshire followed with a 5% rate. Bradford, and Blackburn with Darwen in Lancashire, were the next highest.
Ashford and Folkestone were in seventh and eighth place respectively. Ashford recorded a figure of 3.9 cases per 100,000 people based on a 14 day rolling average; Folkestone recorded 3.6%.
The figures were leaked to The Guardian, which was told by a public health director that deprivation was thought to be behind the concerning levels in some areas.
"Some are going to be in the list for the whole period of the pandemic. The drivers are structural and demographic, so the pattern of spread will reflect the inequalities that already existed. Some of the most strapped-for-cash councils are going to be dealing with some of the worst outbreaks," they added.
Health secretary, Matt Hancock, announced the UK’s first local lockdown on 29 June as Leicester reported 944 new cases in a fortnight. Non-essential shops and schools were shut, and pubs and restaurants were unable to reopen. Legislation to enforce the restrictions was pushed through parliament.
The classified list of 20 at-risk councils uses six metrics including number of cases per 100,000 of population per week and per day and percentage of individuals testing positive as a proportion of all tests.
The Department of Health and Social Care said it did not have a set trigger, but would use a range of data to decide where and how to act, stating: “We have been transparent about our response to coronavirus and are always looking to improve the data we publish, including the way we update testing statistics.
“The list of the 10 local authorities with the highest weekly incidence of coronavirus is already publicly available in PHE’s weekly surveillance report.
“All councils in England now have the ability to access testing data, right down to an individual and postcode level. If councils feel they require more assistance with data, of course, PHE is able to help them.”
Council leaders in Ashford have previously said high levels of testing could be behind the town's consistently high figures.
Deputy leader Paul Bartlett told KentOnline in May: ""Ashford has been at the forefront of testing for Covid-19, something which the government is keen to encourage, and testing remains a vital weapon in our battle against the pandemic."
The news comes as Boris Johnson hinted it would soon become mandatory to wear face coverings in shops.
The Prime Minister said on Friday that he wanted to be “stricter” on insisting people wear coverings in confined spaces where they are meeting people they do not normally see.