You’ve pretty match nailed it there. A clearance will be subject to the weather (VFR) and the controllers workload both on Gatwick radar (based in Swanwick Hampshire) and at Gatwick tower, but requests like this are accommodated every day and the process is pretty straight forward.
You’ll generally be given a VFR clearance not above 1500’ VFR via Handcross VRP to hold at the southern maintenance hangars (just south of the 26L threshold). You’ll then be asked to report Gatwick in sight.
Once you enter the control zone south of Crawley you’ll be asked to hold at the southern maintenance hangars (your clearance limit) and to contact Gatwick Tower, using your callsign only (they’ll already have been pre-noted of your details and it reduces their RTF loading) on 124.225.
Subject to the arriving and departure traffic the Tower will on initial call confirm whether you’ll need to hold south of the runway or if you’re ‘lucky’ will issue you with a new clearance to cross the threshold of the runway in use (26L or 08R usually) and then route northbound to leave the zone via the Buckland VRP (west of Redhill).
Once safely north of the runway, you’ll be transferred back to Gatwick Director who will monitor your flight until you leave controlled airspace at Buckland.
The service will then probably be terminated (unless you request otherwise) but I’d recommend and early free call to Biggin on 129.4 (Keep a good look out for glider activity at Kenley which will now be close to your route).
Enjoy and let us know how you get on!