Health Secretary Matt Hancock has told Sky News that ramping up testing means a higher proportion of cases are being found.
The weekly number of coronavirus cases in England in late August was the highest since the end of May, according to government figures.
A total of 6,732 new cases were confirmed between 20 August and 26 August – an increase of 6% on the previous week, NHS Test and Trace data showed.
But comparisons between recent and past cases should be made with caution.
The number of confirmed cases is heavily dependent on how many people and who is tested.
This has changed significantly since the start of the pandemic, with the number of tests processed each day increasing substantially.
Community testing has also expanded, whereas previously access was limited to symptomatic patients and key workers.
Earlier on Thursday morning, Health Secretary Matt Hancock said the UK is finding a “higher and higher proportion” of people who have coronavirus.
He told Sky’s Kay Burley that there are “operational challenges from time to time, but the testing system works well”.
Some 69.4% of close contacts of people who tested positive for coronavirus were reached through Test and Trace in the week ending 26 August, down from 77.1% in the previous week and the lowest weekly percentage since the system’s launch.
For cases handled by local health protection teams, 97.3% of contacts were reached and asked to self-isolate in the same period.
In comparison, 59.8% of contacts were reached in cases handled either online or by call centres.
A total of 73,081 people who tested positive for COVID-19 in England have had their cases transferred to the system since its launch in May.
Of this total, 57,368 (78.5%) were reached and asked to provide details of their recent contacts.
Some 13,958 were not reached, while a further 1,755 people could not be tracked down because their contact details had not been provided.