probably best to strip old varnish off with sander and retreat with oil - ikea do one for their solid wood worktops (behandla I think its called) If the top is laminated from strips have they started to come apart?(is water getting between the strips) If so don't know what to advise someone else probably knows more about it than me; at worst, might have to replace the tops. I stripped yacht varnish off a back door and sanded it and used danish oil. The varnish had peeled  and was chipped and flaking and water was getting trapped under it in places so it was grimy grey and crap looking. It may be not so much water standing on your worktop, but getting trapped under the varnish that is doing the damage and started it rotting. Idon't know if danish oil is poisonous to use in a kitchen near food etc
Hope this helps,
Mr Spanton

Mr Spanton, Keith - thanks

Landlord is easy going and wont mind me doing what i need to.

Keith - water does sit on top, but i also think as Mr Spanton says, that the varnish has broken down in spots that is allowing the wood to go nasty black looking, especially around the sink and wroktop edges where it meets the wall.  If i were to sand back the varnish and try some oil, but it did not work out, how easy is it to remove the oil?

cheers again

Greg,

Danish oil can be varnished over once it is completly dry but Tung oil can't. If you can use a random orbit sander with the white abrasive (for paint) to shift the varnish then move on to the red abrasive for wood it should give you a good finish  I wouldn't advise you use a belt sander as it can make a real mess of any surface.

Try Danish oil then you can always varnish if you need to.

Use cutting boards, when preparing food, to protect the surface.