Meg Hillier, the chair of the Commons Public Accounts Committee (PAC) behind a critical report, saying taxpayers were being treated "like an ATM machine" and urging the Government to justify the "staggering investment of taxpayers' money".
The MPs said ministers had justified the vast expenditure on preventing a second national lockdown, but noted England is currently living under its third in questioning the programme's effectiveness.
They also urged the scheme led by Tory peer Dido Harding to "wean itself off" reliance on thousands of "expensive" consultants and temporary staff, with some receiving £6,624 per day.
The committee, which includes Sheffield MP Olivia Blake, said many important stakeholders "at times felt ignored" by NHS Test and Trace (NHST&T).
A number of local councils in Yorkshire became involved after several months to carry out contact tracing in harder-to-reach communities.
The PAC said the NHS programme does publish a significant amount of weekly data, including some that shows full compliance with the self-isolation rules relied upon by the scheme can be low.
But it criticised the data for failing to show the speed of the process from "cough to contact" and therefore not allowing the public to judge the "overall effectiveness of the programme".
"There is still no clear evidence to judge NHST&T's overall effectiveness. It is unclear whether its specific contribution to reducing infection levels, as opposed to the other measures introduced to tackle the pandemic, has justified its costs," the report said.
The MPs also criticised the scheme for struggling to consistently match supply and demand for the service, and therefore "resulting in either sub-standard performance or surplus capacity".
And they said it remained "overly reliant" on contractors and temporary staff after having to initially act quickly to scale up the service rapidly.
The report said the scheme admitted in February that it still employs around 2,500 consultants, at an estimated daily rate of around £1,100, with the best paid consultancy staff on £6,624.
"It is concerning that the DHSC (Department of Health and Social Care) is still paying such amounts - which it considers to be 'very competitive rates' to so many consultants," the report said.
Ms Hillier, a Labour MP, equated the scheme's budget with being similar to that of the Department for Transport.
"Yet despite the unimaginable resources thrown at this project Test and Trace cannot point to a measurable difference to the progress of the pandemic, and the promise on which this huge expense was justified - avoiding another lockdown - has been broken, twice," she added.
"DHSC and NHST&T must rapidly turn around these fortunes and begin to demonstrate the worth and value of this staggering investment of taxpayers' money.
"British taxpayers cannot be treated by Government like an ATM machine. We need to see a clear plan and costs better controlled."
Ms Blake, Labour MP for Sheffield Hallam, said: "I have been contacted by hundreds of constituents over the past year - students stuck in isolation and waiting 14 days for results; doctors and nurses unable to work because they couldn’t get testing slots; people being told their test results were ‘probably lost’; groups of friends not being told to isolate by contact tracers, despite all testing positive.
"This is unacceptable - especially when we know how much money has been poured into this. I really hope the Department listens to todays recommendations, because we are only going to stop these damaging cycles of lockdowns if and when the Government delivers an effective system."
As England's chief medical officer Professor Chris Whitty warned of another "surge" in the virus later in the year, the PAC called for ministers to set out how the scheme will "cost-effectively maintain a degree of readiness".
Interim Executive Chair of the National Institute for Health Protection Baroness Dido Harding said: “NHS Test and Trace is essential in our fight against COVID-19 and regular testing is a vital tool to stop transmission as we cautiously ease restrictions.
"Protecting communities and saving lives is always our first priority and every pound spent is contributing towards our efforts to keep people safe - with 80% of NHS Test and Trace’s budget spent on buying and carrying out coronavirus tests.
“After building a testing system from scratch, we have now carried out over 83 million coronavirus tests - more than any other comparable European country - and yesterday alone we conducted over 1.5million tests.
"We are now rolling out regular rapid asymptomatic testing which is supporting children to go back to school, people to go to work and visitors to see their loved ones in care homes.
“NHS Test and Trace has successfully reached 93.6% of the contacts of positive cases - with 98% being contacted within 24 hours, and the contact tracing service has already reached more than 9.1 million cases and contacts, making a real impact in breaking chains of transmission.”
Chancellor Rishi Sunak's Budget last week included an additional £15 billion for Test and Trace, taking the total bill to more than £37 billion over two years.
Labour's shadow chancellor of the Duchy of Lancaster Rachel Reeves said the report shows the significantly outsourced system has "failed the British people and led our country into restrictive lockdown after lockdown".
"It underlines the epic amounts of waste and incompetence, an overreliance on management consultants, taxpayers' cash splashed on crony contracts, all while ministers insist our NHS heroes deserve nothing more than a clap and a pay cut," she said.
Trades Union Congress general secretary Frances O'Grady said the Government's refusal to increase statutory sick pay had "massively undermined Test and Trace".
Despite Boris Johnson pleading the UK will have a "world-beating" tracing system, experts advising the Government in the Scientific Advisory Group for Emergencies (Sage) said in September that the testing programme was only having a "marginal" impact on transmission.
Whitehall's spending watchdog, the National Audit Office, has also previously criticised the service.
Its report in December said not enough test results were delivered within 24 hours, and too few contacts of infected people were being reached and told to self-isolate.
Some call handlers were also said to have been busy for only one per cent of their paid hours in the service's early days, rising to less than 50 per cent in October.
The Government has been approached for comment about the PAC report.