The ride-hailing firm has faced protests in several cities across the UK, with riders choosing to switch off their apps and make themselves unavailable for work.
James Farrar, head of the United Private Hire Drivers, told the BBC: "In the history of our union, I've never seen anything quite like it."
The Independent Workers Union of Great Britain has called on Uber to honour an employment tribunal verdict in 2016, which rejected the firm's assertion that drivers are self-employed.
However, Uber has defended its record, saying it has introduced a variety of different benefits for employees over the last few months.
Meanwhile, Uber was recently ordered to pay $148 million to settle a legal dispute over a cyber-attack that exposed the information of more than 50 million customers and drivers.
The security breach at the ride-hailing company occurred two years ago, but Uber tried to hide the incident from industry regulators, and then decided to pay the hackers $100,000 to delete the data they originally seized.
Following the settlement, the company pledged to change its approach to data in a bid to avoid a repeat of the incident.