The government has drawn up a list of 20 councils facing the worst coronavirus outbreaks in England, with Bradford, Sheffield and Kirklees identified as areas needing “enhanced support”, according to a classified document leaked to the Observer and the Guardian.

As evidence mounts that the relaxation of lockdown rules is leading to a resurgence of Covid-19 in some of England’s most deprived and ethnically mixed areas, officials have ordered the army to deploy extra mobile testing units, which will be sent into a series of hotspots around the country from this weekend.

Public Health England (PHE), the country’s lead infection control agency, briefed local government health chiefs last week that ministers were considering publishing a ranking of the 10 councils most affected by new outbreaks, which could be released within days. Councils fear the data will be used to enforce more local lockdowns of the kind imposed in Leicester, where all but essential shops must stay shut, schoolchildren have been sent home, and pubs and restaurants remain closed.

The top 10 ranking is likely to be based on a document circulated to local health chiefs on Thursday, headed “official sensitive”. The chart, compiled by PHE and reproduced here, ranks the 20 councils with the highest proportion of positive cases. Leicester remains at its head, with 5.7% of individuals who underwent a test found to have the virus. Kirklees, in West Yorkshire, was not far behind, with a 5% rate. Bradford, and Blackburn with Darwen in Lancashire, were the next highest.

Titled “local authority areas of interest”, the table is based on testing between 21 June and 4 July. It identifies six areas of “concern”. More serious cases are labelled as needing “enhanced support”, with three councils in this category. One – Leicester – is listed as requiring “intervention”.

The document states “these areas are currently under investigation by the local public health protection teams”. “Testing access is being increased in areas including Bradford”, it says, and the areas listed are “associated with workplace outbreaks which have contributed to the increase in infection rates”.

Last month, 164 workers at a meat factory in Kirklees tested positive, and at the beginning of July, a bed factory in Batley, which is administered by Kirklees Council, was closed after eight workers were found to have the virus.The communities most affected have several factors in common: poverty, poor health and a high proportion of non-white residents.

The top 10 is likely to change daily, although some areas will remain severely affected for weeks, health directors believe.

“Those on the list are going to be characterised by higher deprivation, higher black, Asian and minority ethnic (BAME) communities and denser housing,” said a public health director briefed on the plans.

“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.”

Areas with large south Asian populations, particularly where several generations may share a home and live in crowded conditions, are among those emerging as particularly at risk.

Bradford has the highest proportion of people of Pakistani origin in England.

The council has today deployed testing units, staffed by the armed forces, to its Bowling and Keighley districts. Residents will be able to be tested without an appointment. Similar units will be deployed in Blackburn and Sheffield.

“Bradford has a higher infection rate than most but it’s coming down due to action we’ve taken,” said council leader Susan Hinchcliffe. “We welcome the dialogue with government. We’re already doing more testing than any other authority in the region, but want to do more.”

Bradford has asked for its own mobile testing units, more environmental health officers, support to pay full wages to low-paid workers having to self-isolate, and funding to develop its own local test-and-trace system.

Officials have not yet outlined what metrics will be used to impose further lockdowns, but it is understood a system based on the German model is under discussion. This would involve a threshold of 50 weekly positive tests per 100,000 of the population in any given council. Once that is breached, special measures could be triggered.

Data made public on Thursday shows Leicester is currently on 116 new cases per 100,000 of population per week, down from 140 two weeks ago.

Rochdale is in second place, with nearly 33 cases, down from over 50 three weeks ago. Kirklees is also suffering high rates, as are Bradford, Blackburn with Darwen, Rotherham and Bedford.

The 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.

Desperate to avoid Leicester’s fate, councils are lobbying for a “graded response”, the local public health director said, with a rolling back of some elements of lockdown, such as larger gatherings, rather than closure of whole sectors. “What we want to avoid is the secretary of state making clumsy, unhelpful interventions, so we are getting ahead of the curve, understanding what our problem is and acting to address it. But we are hampered by slow reporting of data and absence of data,” they added.

Councils have only just begun to receive a breakdown of new cases by postcode, and this is arriving weekly. Health chiefs say they need the information daily if they are to spot outbreaks in time to stop them spreading.

The plans to publish a top 10 were discussed on a regional call with Public Health England, two public health directors confirmed. “They seem to be intent on putting it into the public domain,” said one of those on the call. “We have expressed some concerns over how they do it, as the data does need to be interpreted. Nonetheless, I welcome transparency.”

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, percentage of individuals testing positive as a proportion of all tests, and “exceedances”. This is where councils are issued with a red light because they consistently have more positive cases than forecast by a government algorithm. A slightly lower number of exceedances leads to an amber light.

The chart also shows the number of community outbreaks per council over the last week. Outbreaks are classed as two or more positive tests in a single setting, such as a workplace, school or prison.

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.”

Kirklees and Sheffield councils were approached for comment.