We wanted a self-drive minivan dropping at Gatwick (for 8 of us), but none of the car hire firms with depots at Gatwick (Avis, Hertz, National and Europcar) hires anything bigger than a Galaxy or Espace. We telephoned them all just last week.
We are travelling from Leeds to Gatwick in November, (party of 6) and have managed to obtain a one-way drop-off with e-Sixt Car Hire (formerly Kennings). Try this link to their web site.
Whilst you may not find a large mini bus on the site, contact their national booking number as I do know that they do have (or had) 8 and 18 seater mini buses for hire.