Around four in 10 contacts of people testing positive for Covid-19 are still not being reached through the Test and Trace system.

Some 60.5% of close contacts of people who tested positive in England were reached in the week ending November 11, according to the latest data from the Department of Health and Social Care.

It is the fifth week in a row that the figure has been just above 60% – meaning a little under 40% of contacts continue to be missed.

The proportion of contacts reached through Test and Trace has fallen gradually since the scheme was launched at the end of May, when the figure stood at 91.1%.

For cases managed by local health protection teams, 98.9% of contacts were reached and asked to self-isolate in the week to November 11.

For cases managed either online or by call centres, 58.9% of close contacts were reached and asked to self-isolate.

Downing Street defended the “colossal” achievements of Test and Trace but acknowledged improvements could be made.

A No 10 spokesman said: “We are testing more people per head of population than any other European country and that will grow thanks to our increased testing capacity.”

But “we accept there are still improvements to be made, and we will continue to work on it”.

The latest figures also show that 167,369 people tested positive for Covid-19 in England at least once in the week to November 11.

This is the highest weekly number since Test and Trace began, and is an increase of 11% in positive cases on the previous week.

Some 9.6% of people tested had a positive result, similar to the 9.7% reported the previous week.

A total of 38% of people who were tested for Covid-19 in England in the week ending November 11 at a regional site, local site or mobile testing unit – a so-called “in-person” test – received their result within 24 hours.

This is up slightly from 37.5% in the previous week.

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.

He told the House of Commons on June 3 that he would get “all tests turned around within 24 hours by the end of June, except for difficulties with postal tests or insuperable problems like that”.

Of the 156,853 people transferred to the Test and Trace system in the week to November 11, 84.9% were reached and asked to provide details of recent close contacts.

This is down slightly from 85.6% in the previous week, which was the highest weekly percentage since Test and Trace began.

Some 13.7% of people transferred to Test and Trace in the week to November 11 were not reached, while a further 1.4% did not provide any communication details.

Baroness Dido Harding, interim executive chairwoman of the National Institute for Health Protection, said: “This week we have seen more tests processed and more positive cases contacted than ever before, which means we are finding the virus where it hides and reducing its spread.

“As the number of people using Test and Trace continues to increase, so the service is constantly evolving and improving.

“This week sees the introduction of changes to the contact tracing programme to reduce calls to the same family household, which should reduce duplicate calls, as well as the introduction of Sunday collections of tests from priority boxes by the Royal Mail, which should improve home test turnaround times.

“Meanwhile, our commitment to increasing capacity continues, with our announcement this week of two new ‘mega labs’ that will see testing capacity grow by 600,000 a day by next year, while generating local employment.”