A total of 6,732 people tested positive for Covid-19 in England in the week to August 26 – the highest seven-day number since the week to June 3.
It also marks a six per cent in infections on the previous week, according to the latest Test and Trace data.
The figures were released after Health Secretary Matt Hancock acknowledged that a second spike in the pandemic remained possible in Britain.
He told BBC Radio 4's Today Programme on Thursday that while efforts to curb transmission are "going well", authorities remained "very worried" about a potential second wave.
Since the launch of the Test and Trace programme in England in May, 270,559 close contacts of people who have tested positive for the virus have been reached and asked to self-isolate.
This is 79.7 per cent out of a total of 339,635 people identified as close contacts.
Some 69.4 per cent of close contacts were reached through the system in the week ending August 26, according to new figures from the Department of Health and Social Care.
This is down from 77.1 per cent in the previous week, and the lowest weekly percentage since Test and Trace began.
For cases handled by local health protection teams, 97.3 per cent of contacts were reached and asked to self-isolate in the week to August 26.
By contrast, for those cases handled either online or by call centres, 59.8 per cent of close contacts have been reached and asked to self-isolate.
Meanwhile, Mr Hancock has insisted that the Test and Trace system is "working well".
He told Sky News: “At the moment the system works well. Of course there are operational challenges from time to time but it works well.
“And we’re finding a higher and higher proportion of people in the country who have coronavirus and getting them tests so they can be looked after.
“But absolutely, we need to roll out more testing – we have done throughout this crisis and today’s another step in solving some of those problems with the existing technology.”
According to the new figures, 73,081 people who tested positive for Covid-19 in England have had their cases transferred to the NHS Test and Trace contact tracing system since its launch.
Of this total, 57,368 people (78.5 per cent) were asked to provide details of recent contacts while 13,958 (19.1 per cent) were not reached at all.
A further 1,755 people (2.4 per cent) could not be contacted because their communication details had not been provided.
The figures cover the period May 28 to August 26.