"We hope to continue having constructive discussions with Transport for London", Uber said Friday in an emailed statement. A hearing is likely to take place on December 11, a spokesman at Britain's Judicial Office told Reuters.
Uber was required to begin its appeal by Friday or it would not be allowed to continue operating in London.
Uber has appealed the decision to deny it a new operating license in London. In his open letter Khosrowshahi vowed to make things right with for Uber, so that it can still drive through the streets of London.
TfL has highlighted the company's approach to reporting serious criminal offences and to obtaining criminal record checks for drivers as factors in its decision.
"The courts now will consider the appeal from Uber and of course TfL will defend the decision they made", he said (via Reuters).
His predecessor, Travis Kalanick, left the company following allegations that managers didn't adequately address reports of sexual harassment.
Following the ruling, Uber's CEO Dara Khosrowshahi apologised to Londoners on behalf of the company.
Uber has been used by 3.5 million Londoners, developing a loyal fan base by offering convenience and lower prices than traditional "Black Cabs".
Khan, a politician from the opposition Labour Party who is also chairman of TfL, has long criticised Uber's British management and backed the regulator's decision on Thursday.
An online petition to "save" Uber has garnered over 850,000 signatures.