The row relates to new minimum rates being introduced by Uber, the European app-based private hire operator which is no stranger to controversy.
The firm is cutting minimum fares by 13 per cent in a bid to boost passenger numbers and dominate the huge market.
It claims drivers’ hourly earnings will actually go UP - but has promised to “re-assess” the situation if that doesn’t happen.
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However drivers claim the opposite - and that their cars will become “rolling sweat shops”.
The calls earlier today (Friday) were led by the United Private Hire Drivers (UPHD) union. It wants Leeds City Council to step in and cap all private hire driver numbers. As well as lobbying the authority, it claims support from Leeds MP Hilary Benn and Naz Shah from Bradford West, as they fear the issue will spread across other West Yorkshire and Lancashire cities.
James Farrar, co-founder of UPHD, said: “No fair minded person can condone working conditions little better than rolling sweat shops in 2016 Leeds.
“Certainly, we should not expect an elected city council to preside over such an exploitative system.”
Nadeem Iqbal, UPHD West Yorkshire Organiser, added: “Leeds drivers are crying out for the city authorities to step into what has become an increasingly out of control, unsafe and unfair operating environment.
“Every day I meet drivers now facing debt and despair as they struggle to keep up with their fixed costs while their incomes fall due to falling fares and a flood of new drivers who Uber have promised riches to.”
Max Lines, from Uber, said: “We want the thousands of drivers who use our app to have more fare-paying passengers in their car for each hour on the road.
“That’s why, to encourage more people to use Uber to get from A to B, fares were reduced in West Yorkshire.
“It’s early days but the impact of the first couple of weeks of this change is really encouraging.
“Cheaper fares have seen more people using Uber to get around and the result is hourly payments for drivers have gone up by 2.5 per cent compared to the week before the price change.
“We believe these changes will continue to mean drivers are busier, but while the city adjusts to the new prices we have put in place minimum payment guarantees.
“Drivers using our app in Leeds are getting average payments of £12-13 an hour after Uber’s service fee. And, as we said at the outset, if the amount partner-drivers make on the road isn’t what we expect, we’ll reassess this price change.”
Councillor Mary Harland, chair of Leeds City Council’s licensing committee, said: “We are aware of a number of concerns raised by license holders regarding Uber and have arranged to meet with the organisers of today’s protest to listen to their concerns first hand.
“We will then consider the matter further and then take any action as necessary.”