How to seal a water tap

Are you sure it's actually leaking from the bottom seal and not just flowing down from the top seal connected to the cistern? To be sure run your dry hand around the pipe near the top seal.

In any case to replace any of those seals:

1. Turn off the inlet tap to the cistern and flush until no more water remains in the cistern. (Have some rags ready anyway as there's bound to be a small amount of water coming out residual to the cistern.)
2. Undo the nut at the cistern end by hand and lower this end of the pipe--now you can slide it back towards the cistern to remove it from the bowl.
3. Replace any broken seals and reinstall (reverse of removal instructions).
4. Open the water to cistern inlet and flush several times to check for leaks. Make sure both the cistern and bowl are well secured as any possible movement left may cause leak during usage.

It should not be necessary to try to goop some type of sealer around the lower neck of the sink drain. Such solution may work but it is not the desirable approach when you consider that someday this assembly will need to come apart for repairs.

In looking at the assembly that you have I wonder if one or more things are at play here.

1) If the drain pipe tail was not centered in the neck of the sink drain and then had lateral force on it due to the down stream goose neck trap it could be forcing the gasket open on one side. Check that there is no undue large amount of sideways pressure on the lower part of this pipe assembly.

2) It looks like the gasket directly contacts with the face of the capture nut around the drain pipe. It is possible that by tightening the capture nut that it is putting a twisting force on the gasket that may cause it to "fold away" from the sealing edge of the sink neck.

3) It is possible that there could be a small crack or pitted area on the sink neck that keeps the rubber gasket from engaging 100% with the sink neck.

4) Sometimes the "rubber" used in this type gasket is made of a plastic material that is anything but rubber. Check at the local hardware store to see if they have another gasket that is more pliable. In some cases a silicon material may be better.