The ride hailing startup's licence in the capital is up for renewal in May and a group representing cabbies are opposing its renewal.
The Licensed Taxi Drivers Association (LTDA) has written to the transport operator which regulates the taxi and minicab industry, setting out what it believes are the legal arguments against it being given fresh permission.
It argues that Uber drivers are "plying for hire" by using the app, something it is illegal for minicabs to do, that the startup is failing to ensure passenger safety and does not pass the "fit and proper" standards required.
"Unless Uber starts acting like a fit and proper operator, playing by the rules and putting the safety of its passengers ahead of profit, it should not have its licence renewed," said LTDA boss Steve McNamara.
“Since Uber began operating in London, it has challenged any and every attempt by TfL to regulate it and protect passengers and the wider public. It also continues to blatantly flout the two-tier system of regulation by encouraging its drivers to ply for hire."
It's the latest twist in the long-running battle between the black cab industry, Uber and TfL.
Previous rows have ended up at the High Court, where a judge ruled the Uber app does not break laws on taximeters in 2015.
A second separate case this year saw TfL win in its bid to introduce English language tests for drivers, though it was forced to drop other plans for governing Uber in the capital. TfL has since pushed back plans for English Tests and is still facing pushback from London Assembly members, who last month sided with Uber, saying the rules are disproportionate. Uber is also appealing the decision.
Transport for London last week proposed new rules for how much Uber and other private hire operators will have to pay for a licence. The cost could rise from just under £3,000 to more than £2m for Uber and Addison Lee, which TfL will use to cover the costs of enforcing regulation.
A spokesperson for Uber responding to the LTDA's letter to TfL, said: "Millions of Londoners rely on Uber to get a convenient, safe and affordable ride at the push of a button and thousands of licensed private hire drivers make money through our app. More choice for consumers is a good thing and we believe that black cabs and apps like Uber can and should live side by side."
A TfL spokesperson said: “We do not comment on the status of individual licence applications.”