Unless things have changed you didn't need a permit you can just go! If you are taking a horse box you need to ring to 'pre-book' mainly for space purposes. My old yard backs onto the golf course so we just had to ride over our back fields to get there, it's lovely to go round just watch out for the golf balls!
I am at a yard in Chelsfield and ride over Lullingstone quite often. No permit is required to ride there. You must follow the bridlepaths but there are some good canters. If you box there you now have to pay a charge to park it although I can't remember how much - probably something like £5.
It can get a bit busy over there sometimes with walkers and their dogs and/or children and also bicycle riders as well as the golfers but as long as you are polite and considerate of the other users then they are too.
I never knew you could ride at Lullingstone! As sprog's boyfriend plays cricket in Eynsford, think we'll take the ponies over and go for a hack leaving the OH's to drink beer/watch paint dry!