Some 68.6 per cent of close contacts of people who tested positive for Covid-19 in England were reached through the system in the week ending September 30.
This is the lowest weekly percentage since Test and Trace began, and down from 72.5 per cent in the previous week.
For cases handled by local health protection teams, 97.1 per cent of contacts were reached and asked to self-isolate in the week to September 30. For those handled either online or by call centres, 62.4 per cent of close contacts were reached and asked to self-isolate.
Of the 34,494 people transferred to the Test and Trace system in the week to September 30, 74 per cent were reached and asked to provide details of recent close contacts.
This is the lowest percentage since the first week of Test and Trace in June, when the proportion reached was 73.4 per cent.
The data also shows that 25.7 per cent of people who were tested for coronavirus in England in the week ending September 30 at a regional site, local site or mobile testing unit received their result within 24 hours.
This is down from 38 per cent in the previous week, and is the lowest weekly percentage since June.
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.
Overall, 51,475 new people tested positive for Covid-19 in England in the week to September 30, according to the latest figures.
This is an increase of 56 per cent in positive cases on the previous week and is the highest weekly number since Test and Trace was launched at the end of May.
When it comes to the percentage of positive cases out of the total people tested, the latest data shows a positivity rate of 9 per cent.
There were 51,475 positive cases out of a total 588,895 people tested.
Rowland Kao, professor of veterinary epidemiology and data science at the University of Edinburgh, said the positivity rate and the fact that test numbers are not increasing may be a "troubling indicator" that Test and Trace is not keeping up with demand.
Meanwhile, the chief executive of NHS Providers, Chris Hopson, said: "It is very worrying to see such a large increase in the number of people testing positive with Covid-19.
"Trust chief executives across the North West, North East and Yorkshire are telling us that Covid-related hospital admissions are rapidly rising as well.
"We need prompt action to prevent a full-blown second Covid surge.
"We need to make difficult decisions now, rather than later, when it may be too late."
He added: "And we need every single member of the public to play their part – hands, face and space – as they did in the first phase of Covid, however frustrating and burdensome they find any restrictions or public health advice.
"It’s also worrying that NHS Test and Trace performance in key areas such as the proportion of positive cases transferred into the Test and Trace system, of close contacts reached, and of tests turned round within 24 hours, are all getting worse when we need them to get better, quickly.”
The latest data shows that nearly a quarter of the 51,475 people who tested positive for Covid-19 in England were aged 10 to 19.
People aged 20 to 29 accounted for 24 per cent of new cases.
This means in total nearly half (46 per cent) of cases in that week were people aged 10-29 – the highest proportion for this combined age group since Test and Trace began.
Interim executive chairwoman of the National Institute for Health Protection, Baroness Dido Harding, said: "As the number of cases rise, so demand for tests continues to grow.
"We are working hard to increase testing capacity to meet that demand and improve turnaround times for tests.
"The announcement today of new partnership agreements with four London university labs will see tens of thousands of extra tests being processed over the coming months and into the new year.
"We have now opened 500 test sites across the UK, an extraordinary achievement."
The Department of Health and Social Care said there are now 87 local authority contact tracing teams live across the country, with more due in the coming weeks.