Cabbies have rejected an offer from Uber which would allow them to use the taxi-hailing app for nothing for a year.
Uber presented the offer as an attempt to improve its relationship with London's cabbies.
But a cab drivers' association said it would be "amazed if any drivers decide to take up Uber's offer".
And rival Hailo described the offer as "posturing", saying it doubted the move would calm matters.
There has been friction between Uber and some cabbies, who have said the app is "unfair competition".
Uber said that from Tuesday, it would waive its 5% commission for black taxis for a year.
Jo Bertram, regional general manager of Uber in the UK, said: "London's cabs are famous the world over because they are an iconic part of our city's transport infrastructure.
"It's why the impact of apps like Uber on traditional taxis has generated such a heated debate in the capital.
"We believe that black cabs and Uber can coexist."
Ms Bertram said in a blog post that the Knowledge, which requires four years of study by aspiring black cab drivers to memorise London streets and landmarks, was "an onerous test" which could be completed more quickly in "the age of GPS and live traffic apps".
But Steve McNamara, general secretary of the Licensed Taxi Drivers Association (LTDA), said: "With over 15,000 cabbies registered with specific taxi-hailing apps like Gett and Hailo, we would be amazed if any drivers decide to take up Uber's offer."
He said the Uber offer was "just another PR stunt from a company that spends £250,000 every month on lobbying and PR".
"The response is 'Thanks, but no thanks'," he added.
The offer has been launched on the eve of a planned protest by cabbies affiliated with a separate drivers' association, the United Cabbies Group.
Mr McNamara said the protest had not be organised by LTDA, but that "cabbies have a right to make their voices heard".
Len Martin, chairman of the United Cabbies Group, said: "The taxi trade neither want nor welcome any such offer from an outfit that will tarnish our reputation by association."
A number of protests against Uber have been held by taxi drivers around the world, including protests in London.
Hailo chief executive Andrew Pinnington told the BBC that given the history of the relationship between Uber and black cabs, he doubted that cabbies would take up the offer.
He said Ms Bertram had appeared to offer an olive branch, but in fact had "called into question" the Knowledge, which cabbies hold dear, and also the vehicles themselves.
"Uber will have come under a lot of pressure around the globe because of challenges to incumbent bodies," he said. "There's an element here of posturing."
"They [Uber] are trying to send out the message, 'We are doing our best to reach across,' but I don't think there is serious intent."
Hailo is one of the major ride-hailing apps used by black cabs in London. Mr Pinnington said about 15,500 cabbies used the app, out of a total of 25,000.
Of the black cabs that use Hailo, on average between 15% and 20% of their work comes through the app, he added.