Just 59.6% of close contacts of people who tested positive for Covid-19 in England were reached through the system in the week ending October 14.
Speaking at a coronavirus update from Downing Street, the prime minister said: “I share people’s frustrations and I understand totally why we do need to see faster turnaround times and we need to improve it.
“We need to make sure that people who do get a positive test self-isolate – that’s absolutely crucial if this thing is going to work in the way that it can.”
Sir Patrick said the uptick in cases seen across the country meant the system was under more pressure, and therefore not as effective as if there were fewer cases.
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.”
The test and trace figures represent a fall from 63% of close contacts traced, which at the time was also a record low.
A total of 101,494 people tested positive for Covid-19 in England at least once in the week to October 14, according to the figures.
This is an increase of 12% in positive cases on the previous week and is the highest weekly number since Test and Trace was launched at the end of May.
The press conference followed an announcement by the chancellor of three new financial support measures which he said would help the UK "through the difficult winter months ahead".Mr Sunak earlier told MPs that:
Hospitality, leisure and accommodation businesses operating under Tier 2 restrictions will be able to apply for grants worth up to £2,100 a month.
The Jobs Support Scheme is being made "simpler and more generous", with staff only needing to work one day a week to be eligible - rather than a third of their regular hours - and the contribution employers make is being reduced from 33% of unworked hours to 5%.
The Self-Employment Income Support Scheme is being doubled from 20 per cent to 40 per cent, meaning the maximum grant will increase from £1,875 to £3,750, over three months.
The self-employment scheme is likely to cost around £3.1 billion over three months.
The increased Jobs Support Scheme is estimated to cost £1 billion a month, if 2 million people claim.
And the grants for Tier 2 businesses are estimated to cost around £200 million a month.