Matthew Taylor, whose report is out on Tuesday, said cash jobs like window cleaning and decorating were worth up to £6bn a year, much of it untaxed.
Instead, the work should be paid through "payment platforms", Mr Taylor told BBC economics editor Kamal Ahmed.
The review, commissioned by Theresa May, also tackles low-paid work, zero hours contracts and the gig economy.
Mr Taylor, who is chief executive of the Royal Society of Arts and a former Tony Blair advisor, is set to call for cash jobs to be paid through platforms such as credit cards, contactless payments and PayPal.
This would make it harder for customers and workers to avoid paying tax.
The recommendations are part of a much wider review into modern working practices, including the gig economy.
Mr Taylor's report recommends a new category of worker called a "dependent contractor", who should be given extra protections by firms like Uber and Deliveroo.
It also says low-paid workers should not be "stuck" at the minimum living wage or face insecurity.
Speaking at its launch, the prime minister will say the Taylor report confronts issues that "go right to the heart of this government's agenda and right to the heart of our values as a people".
Mrs May will say: "I am clear that this government will act to ensure that the interests of employees on traditional contracts, the self-employed and those people working in the 'gig' economy are all properly protected."
In particular, Mr Taylor's review found the UK has a "great record on creating jobs" but less so on the "quality" of those jobs.
"In my view there is too much work particularly at the bottom end of the labour market that is not of a high enough quality," Mr Taylor told the BBC.
"There are too many people not having their rights fully respected.
"There are too many people at work who are treated like cogs in a machine rather than being human beings, and there are too many people who don't see a route from their current job to progress and earn more and do better," Mr Taylor said.
However, Labour's shadow business secretary Rebecca Long-Bailey said the review did not go far enough for the 4.5 million people in insecure work.
"Put simply, today's Taylor report shows that Theresa May is failing working people across the country," she said.
Trade unions also said Mr Taylor did not tackle many of the issues facing workers.
TUC general secretary Frances O'Grady said: "From what we've seen, this review is not the game-changer needed to end insecurity and exploitation at work."
Tim Roache, GMB general secretary, called it a "disappointing missed opportunity".
Mr Taylor, who worked on the review for nine months, is presenting seven recommendations to the government to provide "good quality work".
The BBC understands he will also suggest ways to tackle tax avoidance from cash-in-hand work.
Last year, tax dodging by people in the "hidden economy" cost the government £4.4bn, according to HMRC figures.
However, making changes to cash-in-hand work is a controversial area.
In 2012 the then-Treasury minister David Gauke was criticised for saying it was "morally wrong" to pay tradesmen in cash.
Former shadow chancellor Ed Balls also came under fire for suggesting people should get a written receipt for all transactions, even small gardening jobs.
Source: BBC News