The prime minister for the first time acknowledged failings in the service, which is run by Tory peer Baroness Dido Harding, after it posted its worst ever contact tracing figures this week.
Chief scientific adviser Sir Patrick Vallance meanwhile warned that the so-called NHS Test and Trace service, which has been criticised for its level of outsourcing of the service to private firms like Serco, was becoming less effective as coronavirus cases rise.
It came after figures showed the controversial system saw just 59.6% of cases in England being reached and told to self-isolate to stop the spread of the virus, some way short of the 80% target needed for it to work effectively.
Johnson told a No.10 Covid briefing: “I share people’s frustrations.
“We do need to see faster turnaround times.
“We need to improve it.
“We do need to ensure that people who get a positive test self-isolate.”
Vallance admitted there was “room for improvement” in the NHS Test and Trace system.
He said: “It’s undoubtedly the case that test, trace and isolation becomes much more difficult to have an impact once numbers are high. It’s much more effective when numbers are low.”
The number of tests able to be carried out had increased but “it’s really important to concentrate on numbers of contacts, isolation, as quickly as you can, and getting things back as quickly as you can – ideally you get the whole process done within 48 hours.
“It’s very clear there’s room for improvement on all that and therefore that could be diminishing the effectiveness of this.”
Later, Vallance said the service would only be effective in areas with lower rates of transmission rather than those with high levels of Covid like Merseyside or Manchester.
“Test and Trace will work effectively across parts of the UK where cases are lower, that’s when it can work most effectively.
“It has much less of an impact in the areas where you have got very high levels and that’s why additional measures are taken.
“That’s why additional isolation measures... having to take difficult decisions around premises that need to be shut and so on, that’s why they are taken, because you can’t really control it any other way than by stopping contacts.”