According to the study, "weak deterrents" and "excessive centralisation" have made NMW enforcement "ineffectual".
The warning comes less than a month after the Government launched a support service to help workers who are underpaid and announced it is cracking down on rogue employers who fail to pay staff the minimum wage.
The study found more than 300,000 people in the UK earn less than the NMW, but only nine employers have ever been prosecuted for underpaying.
The Government said any employer found to be paying staff under the NMW will be "named and shamed". It hoped the bad publicity would be an additional deterrent to businesses.
Bharat Mehta, the chief executive of Trust for London, said: "The face of poverty in the UK is changing with low pay and in-work poverty increasing. Too many people doing valuable work are getting stuck and not earning enough to live a decent life."
The study has recommended a number of reforms:
- Local authorities should be granted greater powers to tackle minimum wage non-compliance.
- Removing the £5,000 limit on fines levied against employers paying below the NMW.
- Banning the advertising of unpaid internships.
- Insisting on NMW payment for home carers' travel time.
The report's author, Andy Hull, said even though the NMW has changed millions of lives since its introduction 15 years ago there are still too many workers paid below it.
"We are proposing a series of ways to increase compliance with the minimum wage and enhance enforcement of it. After all, it is meant to be a right, not a perk," said Hull.
TUC general secretary Frances O'Grady said: "There must be no hiding place for employers who try to cheat workers out of a legal wage and bosses who avoid paying the minimum wage should face prosecution, naming and shaming, as well as tough financial penalties.
"While hard-pressed HM Revenue and Customs staff regularly recover more than £3 million a year for workers on illegal poverty pay, it is clear that far too many unscrupulous bosses are still getting away with ignoring the minimum wage. This means that around 300,000 workers across the UK are not being paid what they should be."
In October, the NMW increased by 12p to £6.31 an hour, and by 5p to £5.03 an hour for 18 to 20-year-olds.