The case concerns the legal concept of "passing off" - cashing in on someone else's good name and reputation.
In the latest round of a dispute expected to run up of pounds 500,000, the Knightsbridge store is challenging a High Court ruling by Mr Justice Harman two years ago that it was not entitled to an injunction.
The school was established in September 1993 in the old Harrods staff club building in Barnes, south-west London.
Mr Justice Harman ruled that parents of prospective pupils had not been confused into thinking it was connected with Harrods. But Charles Sparrow QC argued yesterday that there was a monopoly in a name if it had years of goodwill and reputation attached to it. The hearing continues today.Reuse content