Between 24 and 30 September, 51,475 people tested positive for COVID-19 - a 56% increase compared with the previous week and the highest total since the scheme was launched at the end of May.
Meanwhile, two-thirds of positive cases - 34,494 people - were transferred to the contact-tracing system.
Some 68.6% of their close contacts were reached, making it the lowest weekly percentage since Test and Trace began and down from 72.5% the previous week.
Local health protection teams were much more successful in reaching close contacts, getting hold of 97.1%.
But for cases handled either online or by call centres, only 62.4% of contacts were reached.
Some 2.4% of people who used a home test kit received their result within 24 hours, while 26.5% did within 48 hours.
The statistics come after a technical issue meant nearly 16,000 positive cases were not included in official figures until days afterwards, also causing delays for contact tracers.
By last Tuesday, almost 8,000 cases still had not had their contacts traced.
Prime Minister Boris Johnson has said that a successful Test and Trace scheme should create a "fire break" around positive cases and "help us fight the virus".
Responding to the latest statistics, his official spokesperson said: "We have set up from scratch what is the biggest testing network in British history.
"That includes 96 NHS labs, 258 mobile units, 77 regional sites and 151 walk-in sites.
"Our laboratories are now processing over a million tests a week and we continue to announce new facilities and technology to process results even faster."
It follows new figures from the Office for National Statistics (ONS) which showed coronavirus caused three times more deaths than pneumonia and flu combined in the first eight months of this year.
The UK recorded 14,162 new daily coronavirus cases on Wednesday, according to government figures.
A further 70 people died within 28 days of testing positive for coronavirus, taking the total to 42,515 deaths.
Analysis: Test and Trace is meant to be our main line of defence - its performance is worrying
By Rowland Manthorpe, technology correspondent
The number of positive cases in England has been rising for over a month. This latest set of weekly data shows no sign of the upward trend halting.
One crumb of comfort is the rate of increase.
A jump of 56% is large, but it is some way off doubling every week, let alone every three to four days, as was the case at the start of the pandemic - although remember that this data is for 24 - 30 September, and other signs suggest the rate of growth has increased since then.
More tests will find more cases, of course, but we can take account of that by working out what proportion of people tested end up getting a positive result, a figure known as the positivity rate.
In last week's data it was 5.2%. In this week's it is 8.7%.
The data is very noisy, but the trend is clear, and it is heading in the wrong direction.
A high positivity rate also suggests that you are not catching every case, which is why contact tracing is so important.
Yet, once again, Test and Trace figures show that only 68.6% of overall contacts were reached - a number which disguises even lower rates in some of the worst-hit areas.
That is meant to be our main line of defence, so this is a worry as we look ahead.