Squawk 7500
If such a refusal occurred, next NSL contract to go would be Edinburgh (which the Gatwick owners have a controlling interest?). CAA is not about to allow Gatwick to shutdown due to a lack of ATCOs with LUE, Green Field LUE will be issued following simulator training (all flight procedures in the public domain, via the UK AIP) and airport operator has copies of MATS 2.
NSL already in the handover mode at Brum, cannot imagine they would let the news media view them as prejudicing safety by refusing to facilitate a seamless transition at Gatwick. After Gatwick they should have the process perfected!