Hi L_S,
I don't know the name of the strip, but I can confirm that there definitely is one near Paddock Wood - I ran the Paddock Wood half-marathon earlier this year and the route went right past one end of a farm strip's runway, just as a PA28 took off.
Unfortunately I'm not at all familiar with that part of Kent so I can't even say whether it was north, south, east or west of Paddock Wood itself! I've been trying to find a copy of the race's route on-line but no joy... good luck, anyway!
cbl.