Water stains on solid pine furnature

Depends on the finish. On a wax surface try a hot iron and a piece of kitchen roll.

Wood-effect sticky backed plastic.

I'd put some oil onto a wad of fine wire wool and I'd rub around the area of the stains.After a while the stains will partially disappear and partially blend in with their surroundings. continue outward toward the edges of the panel, lightening the rubbing to feather the effect. When satisfied, wipe of the oil residue with some white spirits and either wax the panel or apply whatever finish you prefer. It won't necessarily look as pristine as when in it's original state but this can be described as character.

Thanks for the reply.

What kind of oil would be suitable for this?

Cheers, M

I'd use linseed oil out of habit but any vegetable oil would do, as you're not going to need to leave much on there. The oil performs 2 functions. It reduces and smooths the scratching effect of the wire wool and it feeds the area of the water marks in such a way as to reduce their contrast with adjacent areas.