1. The slotted waste has one part in the basin which is screwed into the metal part below the basin seen in your photograph.
2. The part in the basin has a fairly wide lip, and between this lip and the upper side of the ceramic basin is a seal. This can be the seal that came with the waste fitting, usually a (fairly useless) foam type washer. Alternatively, the above sink part may have been sealed to the upper side of the basin with Plumber's Mait or silicone.
3. The part below the basin also has a seal between its flanged top edge and the underside of the basin. This is usually a white or black rubber sealing washer.
4. The only reliable way to get rid of that leak is to remove the upper waste fitting, and replace the upper or lower seals or both.
5. If you get a Monument slotted waste tool, you may be able to remove the upper (in basin) part of the waste fitting. This should then give you enough access to replace both seals, although I don't know where you can get the under basin seals.
6. My preference is for Plumbers Mait to make the upper seal. Roll a thin (less than chipolata) "sausage" of Plumber's Mait, and place it in a circle around the upper waste part, under the flange. Screw the upper part into the lower part, and tighten. As the Plumber's Mait squeezes out, remove the surplus with a non-metallic scraper. When finished, last traces can be remove with white spirit. Check that the sealant has not blocked the slots into the hollow basin, which would stop the overflow working.
7. Before trying the above, it might be worth using the tool to just tighten the upper part into the lower. You might be lucky and seal the leak.