An enquiry is a request for information - a question or a set of questions. It is often used in the plural - making a few enquiries about the price of train tickets. An inquiry has to come to refer to an investigation. It is commonly used in the singular - a court of inquiry launched an inquiry into the cause of the explosion. Source 'The right word at the right time a guide to the English language and how to use it'.
That having been said it wasn't a re run of the inquiry anyway it was a high court hearing into the legality of the outcome of the public inquiry.
The alternative if the high court outcome goes against the airport an application to replace the temporary terminal with a permanent terminal of the same capacity - discusions have been underway for some time ( see minutes of the consultative committee )