The claims, launched in the Employment Tribunal by GMB union, alleges a "failure by Royal Mail to pay the Parcelforce drivers the national minimum wage and holiday pay," law firm Leigh Day said in an email.
"We are aware that a case has been filed. We do not comment on ongoing legal cases," a Parcelforce Worldwide spokesman said.
The drivers also claim Royal Mail Group should give them "paternity pay, sick pay and employee protections such as protection from discrimination." The couriers are classed as self-employed and not entitled to the same right as employees, the law firm added.
A first hearing will be held at the Employment Tribunal on Feb. 16.
The Communications Workers Union has been at odds with Royal Mail since April over its plans to save billions of pounds on its pension contributions and has attempted to call a strike.
(This story corrects first paragraph to say the drivers are part of Parcelforce Worldwide, not Royal Mail, and fixes company name to Royal Mail Group Ltd. The story also changes source in third paragraph to "Parcelforce Worldwide spokesman" from "Royal Mail spokesman".)
(Reporting by Noor Zainab Hussain in Bengaluru; editing by David Evans)