* Uber and transport regulator say CEO meeting "constructive"
* Taxi app promises to make things right
* British capital has refused to renew Uber licence
* Transport for London: Focus needs to be on high standards (Recasts after statements following the meeting)
LONDON, Oct 3 (Reuters) - Uber promised to make things right in London after its new global boss had a "constructive" meeting with the city's transport regulator to try to hold on to the app's operating licence in one of its main foreign markets.
Transport for London (TfL), which runs and regulates the British capital's transport system, shocked Uber last month by deeming it unfit to run a taxi service and refusing to renew its licence. It cited the firm's approach to reporting serious criminal offences and background checks on drivers.
Both TfL and Uber described Tuesday's meeting between the Silicon Valley firm's new Chief Executive Dara Khosrowshahi and TfL Commissioner Mike Brown as "constructive," with the dialogue set to continue.
"We hope to have further discussions over the coming weeks as we are determined to make things right in London," an Uber spokesman said.
"Today's constructive meeting centred on what needs to happen to ensure a thriving taxi and private hire market in London where everyone operates to the same high standards," TfL said in a statement.
Uber's licence expired on Sept. 30 but its roughly 40,000 drivers are still able to take passengers until an appeals process is exhausted, which could take several months.
Reuters reported on Monday that Uber's top boss in Britain, Jo Bertram, would be quitting in the next few weeks to take up an undisclosed new role outside the company.
Uber's British management has been criticised by London Mayor Sadiq Khan, who is also chairman of TfL. Khan said the firm needed to spend less time hiring "an army of PR experts and an army of lawyers" and instead address issues raised by TfL.
Khan, a centre-left politician from Britain's opposition Labour Party, approved Tuesday's meeting between Khosrowshahi and Brown, who is in charge of TfL's day-to-day operations.
Khosrowshahi was appointed Uber chief executive in August, replacing co-founder and former boss Travis Kalanick and has promised change at the $70-billion dollar firm.
He is battling to steer a new course for the app, which has faced regulatory crackdowns, court cases, bans and protests around the world, as well as several boardroom controversies.
In a sign of broader problems facing Uber, Khosrowshahi is also expected to call into a contentious board meeting in San Francisco on Tuesday which will look at cutting the influence of Kalanick, sources familiar with the matter said.
The meeting will consider proposals to strip early investors of super-voting power and secure a multibillion-dollar investment. Kalanick, ousted by investors in June, contends that fellow Uber board members are moving too fast on a dramatic restructuring, the sources said.
Trying to repair relations with the authorities in London, Khosrowshahi last week struck a more conciliatory tone in an open letter to Londoners, marking a new approach for a firm that has adopted a combative style to break into closed markets around the world.
"It's ... true that we've got things wrong along the way. On behalf of everyone at Uber globally, I apologise for the mistakes we've made," he wrote in the open letter.
Uber's fate in London will be decided by a judge who will rule on the appeal after it is submitted by Oct. 13.
Uber's competitors are already trying to take its business. London's second-biggest private hire firm Addison Lee said last week it was planning to increase its driver numbers in London by up to a quarter. (Additional reporting by Estelle Shirbon and Michael Holden; Editing by Keith Weir and Mark Potter)