The GMB union is taking a case against logistics firm UK Express, which is based in Birmingham but employs staff across the UK.
The GMB said it believes the drivers fall into the same category as those at taxi firm Uber, and should be classed as workers, not self-employed.
The case is the latest being brought by the GMB to tackle the growing trend of what it calls “bogus” self-employment and gig economy “exploitation”, the Press Association reported.
Maria Ludkin, GMB legal director, said: “This is another case in a long line of legal battles around bogus self-employment.
“Employers might not like paying the minimum wage or giving their workers the protections they’re entitled to in the workplace, but I’m afraid it’s not optional.
“UK Express deliver for some of the world’s largest companies, in this case Amazon.
“The drivers delivering for Amazon, like Uber drivers and delivery drivers for DX, cannot be classed as anything other than employed when you look at the law.
“We don’t get to pick and choose which laws we adhere to and which we don’t like the look of.
“This is a much wider issue than individual companies like UK Express or Uber.
“This is about employment in 21st century Britain.”
It comes after lawyers acting on behalf of around 200 riders with food app Deliveroo prepared the first stage of legal action.
Solicitors Leigh Day said this week that they were preparing to take the first twenty cases to the conciliation group Acas - a required first step before commencing legal action in the courts.
The law firm said Deliveroo riders are recruited by Deliveroo, a process which involves an interview, a trial shift and online tests.
It added that riders are required to wear a Deliveroo-branded uniform and to use a Deliveroo branded box, and are given very specific instructions about how and where they work.
In addition it said they are subject to performance reviews and their terms and rate of pay are determined by Deliveroo.
All those points are likely to feature in its future litigation.
The world of modern work is the subject of a parliamentary inquiry which MPs hope will cast more light on common self-employment practices in the gig economy.
But Katie Mahoney, an employment solicitor at Doyle Clayton, told The Huffington Post UK this week that the delicate nature of such claims could destabilise businesses currently thriving.
“There are two sides to this,” she said. “If you look at an individual’s perspective - you want more rights. If you think about giving all employees in the gig economy full employees’ rights, that would cripple the low margin models that are used.”
“More and more firms in the gig economy are being challenged in this way,” she added. “They will be looking at the level of control - the more autonomous a person is in how they do their job, the more likely it is they are self employed.”