Statistics published by the Department of Health and Social Care (DHSC) on Thursday, showed 69.2 per cent of close contacts of people who tested positive were reached by Test and Trace in the week to September 2.
That figure is down slightly from 69.8 per cent in the previous week, and is the lowest weekly percentage since the initiative launched at the end of May.
It is also far below the Government’s own target for the system to reach 80 per cent of close contacts of a person with a positive Covid-19 test result.
But Baroness Dido Harding, interim executive chair of the National Institute for Health Protection (NIHP), told reporters the system is working.
The Conservative peer, appointed last month to head up the new NIHP, a body set up to replace Public Health England, said: “NHS Test and Trace is working and every week we consistently reach the majority of people testing positive and their contacts.
“We have now reached almost 360,000 people who may be at risk of unknowingly passing on the virus, helping to curb its spread.
“We are doing more testing for the British public than other comparable European countries and we are adding thousands more tests a day.”
The latest figures show the system recorded the highest weekly number of positive tests to date.
A total of 9,864 new people tested positive for Covid-19 in England in the week to September 2, an increase of 43 per cent in positive cases on the previous week.
The system has been criticised in recent days after reports of people being advised to travel hundreds of miles to get an in-person test because slots nearby were unavailable.
Following the rise in numbers of people seeking a test, on Thursday Baroness Harding called on those without symptoms and who have not been advised to get a test not to apply for one.
She said: “For those who don’t have symptoms or haven’t been told they must have a test, we would please ask you to reconsider as it could be taking a test away from someone who really needs it.”
On Wednesday, Health Secretary Matt Hancock said there had been an increase in demand among people not eligible for tests in recent weeks.
DHSC said it was updating its guidance on testing eligibility on Thursday, to make it clear only those with symptoms or who have been asked to get a test should apply for one through the NHS system.
Waiting times for test results to come back have also increased in recent weeks.
Prime Minister Boris Johnson had pledged that by the end of June, the results of all in-person tests would be back within 24 hours.
But in the week ending September 2, a total of 61.9 per cent of people who were tested for Covid-19 in England “in person” at a regional site or mobile testing unit received their result within 24 hours.
This is up from 53.3 per cent in the previous week, but down from 63.4 per cent in the week to August 12.
The latest DHSC data also showed local health protection teams are continuing to have better results reaching contacts, with cases handled by local teams reaching 96.6 per cent of contacts to request self-isolation in the week to September 2.
By contrast, for those cases handled either online or by call centres, 61.3 per cent of close contacts were reached.