The issue with Gatwick is it is a single runway airport with an emergency runway/taxiway.
A planned change from the normal runway to the emergency runway is expected to take about 15 minutes. An unplanned change can take far longer
I'd expect that the runway/taxiway needs to be inspected, approach aids turned on and checked (assuming it has them), taxi lighting patterns and stopbars changed. Clearances to aircraft reissued. Then you've got to get the aircraft in the hold on the ground. Possibly a lower number of movements on single runway operations as well due to a lack of rapid turn offs etc