Check the water pipes going to the sink, and also the waste pipe from the plughole, to ensure that they are watertight, and firmly clamped up. Fill the sink and look underneath whilst it's full. The sink might be cracked (unlikely, but it happens), or the waste/plug pipe may need simply replacing or resealing.
If you haven't changed the pipes, I would seriously consider doing so on a 1996 caravan. For a small outlay, you'll have clean hygienic pipes again, which will allow better draining and water flow, because it could be as simple as the waste pipe harbouring gunge 'smells'. They don't last forever, and the concertina type pipes used for waste, DO keep food debris and gunge inside them.
Hopefully, you'll find your problem. If not, then carry on looking. If it's damp, you HAVE to find it!!
Check outside the caravan, and under the caravan in the kitchen area. It's possible (let's hope not), that the outer strips along the back/sides of the caravan are in need of re-sealing. If that's the case, then don't ignore it. It is potentially serious. A damp meter would help you to find potential damp spots.
Water is nasty when it gets where it shouldn't, it will find it's way in anywhere, and it can be EXTREMELY difficult to find where it's coming from.
Hope this helps you. Ogre.