Travelodge Billingshurst (3 miles)
Travelodge Horsham (5.5 miles)
Premier Inn Horsham (5.7 miles)
Premier Inn Horsham North (6 miles)
Chequers Pulborough (8.3 miles)
Last I checked, there was limited availability in the area.
If you don't need access to electric hook up, you could probably get away with parking up in a nearby lay-by or there is a place called Sumners Ponds nearby that is within walking distance. When I checked on 6th May, they only had grass standings without electric hook up available.