Transport for London (TfL) and Uber are seeking guidance on whether the company's smartphones are considered meters, which are outlawed for private hire vehicles.
The phones use GPS and external servers to calculate the cost of a journey.
A ruling is to be delivered later, but Uber said the outcome would not affect its ability to operate in London.
Originally scheduled to last two days, the case finished early, on Monday, with a judgement reserved until a later date.
The app-based company allows users to order cars via their smartphones, which often arrive within minutes and can cost a fraction of the price of a black cab.
It operates in Birmingham, Manchester, Merseyside, Newcastle, Leeds, Bristol and Sheffield in the UK, and in 60 countries across the world.
London Mayor Boris Johnson said it would be "nuts" to ban the technology behind the app and called for black cabs and private hire companies to work together and "find a balance" for the benefit of the capital.
TfL's barrister Martin Chamberlain said the point of law Mr Justice Ouseley at the High Court must decide was "narrow but difficult".
He said the organisation had not considered the smartphone app unlawful from the outset, but that TfL needed clarification from the court as the point was "arguable".
Mr Chamberlain added: "TfL has formed a view. If the court takes a different view TfL intends to ensure the law as declared by this court is properly enforced."
A spokesman for Uber said: "We are looking forward to getting binding clarity on this issue in the High Court."
Uber London Ltd, the Licensed Taxi Drivers' Association (LTDA) and Licensed Private Hire Car Association (LPHCA) will give their responses in the hearing.
The LTDA is asking the judge to rule that using a smartphone is unlawful as it said along with apps they operate as taximeters and it is not necessary for them to be "physically" attached to a vehicle to break the law.
LPHCA supports the LTDA's position, saying the app "is an attempt to circumvent the statutory prohibition on the use of a taximeter".
The system used in London by app-based taxi service Uber has been called into question in the High Court.