One piece of equipment believed to have been deployed at the airport is the Israeli-developed Drone Dome system, which can detect drones using radar. It can also jam communications between the drone and its operator, enabling authorities to take control of and land the drone.
In a move known as "buzzing the tower", it emerged the perpetrator had taunted airport staff by circling the drone around the building and flashing its lights
A detailed description of the drone, provided by witnesses, meant experts were able to determine the make and model of the machine, which is only available from a handful of locations in the UK.
Police and military experts were deployed to search for the operators of the drones, which reappeared near the airport every time the authorities tried to reopen the runways.
TLDR; There are no sure fire way to track down offender and police mainly relied on informants and traditional detective work of identifying drone and who might have purchased it.
Better coverage is here:
https://www.telegraph.co.uk/news/2018/12/22/gatwick-airport-...
https://www.theguardian.com/uk-news/2018/dec/22/gatwick-dron...