Don't know any specific good deals, but would think that most of the "big boys" work out of Gatwick. However, I had reason to hire a car at home (2 elderly aunts coming to visit and they couldn't get in the back of my convertible. Needed the car for a wedding on a Sunday.
I got a quote from Enterprise (their website says they hire from Gatwick) - Sat 11.30 am - Monday 5 pm £120 (ish) because it was a 3 day rental because of the timings. However, they have a "weekend special" button on their homepage which I clicked. Friday 5pm to Monday 5 pm - £76. They rang as they were leaving their office to tell me they were on their way (no they weren't late), they collected me on Friday evening and took me home on Monday.
I also received a free upgrade - booked a focus/astra similar and got a beautiful Opel Insignia.
An excellent service, all round.
Hope this helps