Not easy to qualify. I have been through Gatwick in 30 mins with bags, sometimes takes an hour and a half.....
Immigration can be a breeze, at other times, a Zoo.
Baggage handling has been contracted out and again can sometimes be 30 mins at others much much longer (most notably weekends and late evening, which will not impact on you.)
The best placed people will be Addison Lee as they are picking up people from Gatwick all the time.
I would just give them the flight details and see them in arrivals.