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Last year, two drivers successfully argued at a British employment tribunal that Uber exerted significant control over them to provide an on-demand taxi service and should grant them workers' rights such as holiday entitlement and rest breaks.
Uber appealed to the Employment Appeal Tribunal which ruled against it earlier this month.
"We have this afternoon requested permission to appeal directly to the Supreme Court in order that this case can be resolved sooner rather than later," said a spokesman.
Uber says its drivers enjoy the flexibility of their work and are self-employed, entitling them in British law to only basic entitlements such as health and safety.