You should be able to park in the car park where the bike shop is. They normally have the restricted height barriers up to allow cars with bikes on the roof to get under and I recall seeing a trailer parked up in there not so long ago. There is a charge to park though.
If you drive into Ellington village itself theres a sharp bend with a small grass triangle and there should be a sign down to the church and caravan park. Its quite a narrow road but at the end of it, about a mile or so theres a car park down there thats hardly used and heads straight onto the bridleway.