Regulator Transport for London (TfL) shocked the Silicon Valley firm last September by refusing to renew its licence, citing failings in its approach to reporting serious criminal offences and to background checks on drivers.
Uber, backed by Goldman Sachs and BlackRock among others and valued at over $70 billion, has faced protests, bans and restrictions around the world as it challenges traditional taxi operators and angers some unions.
Its chief executive Dara Khosrowshahi, who took charge the month before TfL's decision, has pledged to "make things right" in London, and the court case is a test of how far Uber can demonstrate it has changed.
While the appeal process is ongoing, Uber can continue to operate in the city.
The firm has introduced several new initiatives in London since losing its licence, including 24/7 telephone support and the proactive reporting of serious incidents to the city's police. It has also changed senior management.
Uber's lawyer Thomas de la Mare said the company accepted the September ruling and the focus of the appeal should be on its reforms.
"It's no part of our case to say it was wrong. We accept it was right," de la Mare told Westminster Magistrates Court in London. "It's that acceptance that has led to wholesale change in the way that we conduct our business."
The appeal is due to be heard over three days and will hear from witnesses including Uber's UK Chairman Laurel Powers-Freeling, UK Head of Cities Fred Jones and TfL's Interim Director of Licensing Helen Chapman.
'LACK OF UNDERSTANDING'
Uber UK's General Manager Tom Elvidge admitted the company's correspondence with TfL had at times been inaccurate, incomplete and inadequate across a range of issues.
He said inaccuracies in letters sent in 2014 about whether Uber's business model was legal under London's regulatory framework stemmed from a "lack of understanding" on Uber's part, but that new people as well as the new policies would help to avoid a repeat of the problems in future.
In May, Uber appointed a new boss for Northern and Eastern Europe, which includes Britain, after its previous head Jo Bertram quit last year following the decision to strip Uber of its London licence.
After its application for a five-year licence was rejected last year, Uber is now seeking an 18-month one to prove to the authorities that it has reformed.
Judge Emma Arbuthnot may take weeks before making her decision, which is likely to be subject to further appeal by the losing side, meaning the whole legal process could take years.
However, she signalled any renewal of the licence could be for a shorter period.
"I would've thought, if I were to renew the licence, 18 months would be rather too long," she said.
At stake for the U.S. firm is one of its most crucial foreign markets. Of its over 60,000 drivers in Britain, about 45,000 are in London.
Since September's TfL decision, Uber has also been stripped of its licence by the southern coastal city of Brighton, in a decision which it is appealing, and the northern city of York.
It has, however, gained new licences in Sheffield, Cambridge, Nottingham and Leicester.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)