However, I now find that there is a leak from the basin waste outlet.
This
is a metal tube with the "plug hole bit" at one end and a thread at the
other. It came complete with a plastic nut. I put a bit of sealant round
the plug hole bit but just tightened the big plastic nut as much as I
dared. It is around this nut that the leak is occurring.
What is the approved method of sealing this sort of thing?

The best method is a large conical rubber washer that fits over the metal
waste replacing your current arrangement. It is compressed by the nut (and a
supplied washer) and seals the waste in the same way as the less substantial
(but similar in cross-section) rubber washer in a compression (or Universal)
waste pipe fitting.

Plumbers merchants rarely seem to sell them but they are stocked by
Homebase.

When I don't have one to hand, I tend to use Plumbers Mait (a non-setting
mastic that comes in tubs, also useful to set the basin on the pedestal)
between the lip of the grate and the basin, and a bead of decent silicone on
bothe sides of the washer before doing up the nut. Some people partially
tighten the nut, let the silicone cure to a beautifully fitting custom
washer and then fully tighten the next day but I have never found this to be
necessary.

HTH
Adrian