Campaigners are demanding that the cost of renewing Serco's contract – reported to be worth up to £108 million – on August 23 be diverted to boost existing local public health teams.
The Labour Party is among those calling for an end to the agreement, describing the current national programme as “ineffective” and in need of “radical reform”.
It comes after Downing Street announced that the test-and-trace programme is to cut 6,000 call handlers by the end of August in a move towards a more localised approach.
Official figures show that local teams manage to contact 98 per cent of close contacts of people who tested positive for Covid-19 before asking them to self-isolate.
This plummets to 56 per cent of close contacts in cases handled either online or by call centres.
Boris Johnson this week defended the system as having achieved his pledge of being “world-beating”.
But Serco has been accused of “paying people to watch Netflix " after its 10,000 contact tracers only spoke to an average of 2.4 people each.
Shadow cabinet members Jonathan Ashworth and Rachel Reeves have written to Health Secretary Matt Hancock stressing that it’s “not too late” to “put in place new, locally-led contact tracing measures.”
“The stakes are too high to tolerate failure in either the operation or the design of this crucial public service,” they wrote.
“We cannot afford for the test and trace system to continue as it is without rapid reform.
“It is not too late to improve the system.”
Although the Department of Health (DHSC) has made no comment on the fate of Serco’s involvement in the scheme, health officials have announced plans to strengthen regional contact tracing powers in England.
NHS Test and Trace will now provide local authorities across England with a dedicated team of contact tracers for local areas, while 6,000 of national call handlers will be laid off.
In pilot schemes, they have been able to visit people at home where national contact tracers have been unable to reach them.
Officials said local areas will be given “ring-fenced teams from the national service”.
And if the dedicated national team cannot make contact with a person in a set amount of time, the local public health officials can use the data provided by NHS Test and Trace to follow up.
DHSC added that as the contact tracing system becomes “more locally targeted”, NHS Test and Trace will “will reduce current extra capacity and reduce the number of non-NHS call handlers”.
The department added that staff numbers can “quickly be scaled up, or down depending on requirements for the national service”.
Baroness Dido Harding=, executive chair of NHS Test and Trace=, said: “NHS Test and Trace is one of the largest contact tracing and testing systems anywhere in the world, and was built rapidly, drawing on the UK’s existing health protection networks, to stop the spread of coronavirus.
“At the height of the pandemic we ensured the system had extra capacity in place to cope with potential peaks in the virus.
“We have always been clear that NHS Test and Trace must be local by default and that we do not operate alone – we work with and through partners across the country.”
She added: “After successful trials in a small number of local areas, I am very pleased to announce that we are now offering this integrated localised approach to all local authorities to ensure we can reach more people in their communities and stop the spread of Covid-19.”
James Jamieson, chairman of the Local Government Association, said: “A strong national and local partnership is critical for test and trace to work as effectively as possible and it is right that local resources are kept under constant review to ensure everyone involved is able to help stop the virus spreading further.
“Using councils’ unrivalled local knowledge and vast experience of contact tracing within local public health teams is vital in the Government’s national efforts.”
Shadow health minister Justin Madders said: “Labour has been calling for a locally-led contact tracing system for months – it’s welcome that local authorities are now finally being given additional support to tackle the virus in their areas.
“But it’s clear Boris Johnson’s £10 billion centralised contact tracing system is nowhere near ‘world beating’ as he claims and the system is unable to fight local outbreaks successfully.
“A truly effective system would provide all local areas with detailed data sets, ensure people have support to self-isolate if needed, and give local health officials the help and resources they need to lead contact tracing. Ministers must get on – and implement this without delay – it is vital that we get contact tracing working properly.”
All the data from national and local teams will be fed into the same system, the DHSC said.
It added the national service will be cut from 18,000 to 12,000 contact tracers on August 24 with remaining staff deployed as part of dedicated local tracers.