The only one I definitely know about is Singledge Wood, Roger.
But I suspect nearby Eastling Down is really an extension of the same complex. I am sure there are others, as Neil's map hopefully shows.
Brian, it's not about hugging trees, just ensuring that a few particularly valuable ones don't get houses built all over them.
Spinney Wood appears to be another.
http://www.dover.gov.uk/kentcoal/minerstrail/ancientwoodlands.asp
Moreover we are facing the loss of all those ash trees.
This country seems so lacking in any sense of connection with nature it is scary and what is even scarier is that so many people don't even seem to realise that or place any importance on it.