The public will be able to use the data – and an interactive map – to look at figures for their area, although homes of individuals with Covid-19 will not be identifiable from the data.
Previously, testing data has only been made available at an upper-tier local authority level such as Sunderland, South Tyneside and Hartlepool.
The more localised figures to be introducted for England, will be published weekly at first with the aim of updating them daily.
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Public health professionals across each region will also be given positive test data and contact tracing figures every day.
It comes as new NHS Test and Trace data for England shows that the proportion of people receiving their Covid-19 result within 24 hours of being tested at a regional site or mobile testing unit - a so-called 'in-person' test - has fallen week-on-week.
Some 87.7% of people received the result within 24 hours in the seven-day period ending Wednesday, July 8. This was down slightly from 90.7% in the week ending Wednesday, July 1.
Prime Minister Boris Johnson last month pledged to get the results of all in-person tests back within 24 hours by the end of June.
He told the House of Commons at the beginning of last month he would get "all tests turned around within 24 hours by the end of June, except for difficulties with postal tests or insuperable problems like that".
Some 3.3% of people who took a Covid-19 test using a home test kit in the week ending July 8 received their result within 24 hours - up slightly on the previous week (1.8%).
Turnaround times for home tests can depend on when people send their kit back for analysis.
A total of 67.8% of people received their result between 24 and 48 hours after taking the test, down slightly on the previous week (68.8%).
A further 23.2% waited between 48 and 72 hours for their result (broadly similar to 23.0% in the previous week) while 5.6% had to wait more than 72 hours (down from 6.3%).
Since the launch of Test and Trace, 155,889 close contacts of people who have tested positive for Covid-19 have been reached through the tracing system and asked to self-isolate.
This is 84.1% out of a total of 185,401 people identified as close contacts.
The remaining 29,512 people (15.9%) were identified as close contacts, but were not reached.
Executive chairwoman of NHS Test and Trace Dido Harding, said: "Each week there have been sustained improvements in NHS Test and Trace to reach more people and help stop those who may have been in contact with the virus unknowingly passing it on.
"We have made testing and tracing quicker and more accessible, and we remain committed to develop the service further over the coming months."
The Government has said a team based in Newcastle, including NHS clinical contact tracers, are working closely with behavioural scientists to find new ways to engage the public in Test and Trace.
Forcing people to comply with the system has been ruled out for now.