My latest cock-up: Having dug 15M trench, put SWA cable in and
re-filled, I've now discovered it's a 3 core rather than 2 core cable.

Not a cock up. 2 core would have been that.

I could just go ahead and use it anyway I suppose, but since the
core colours are brown, black and grey as for 3-phase system, I
can't use the correct single phase colour scheme - there's no blue.

You probably have used the right cable. It is bad idea to rely on the cable
armour for earthing (obviously it should be earthed, but just not used as
the main earthing conductor). It is much better to have a proper copper
conductor for the earth. I used 3 core for my shed.

You should sleeve the ends of the cable with the appropriate colours where
they are terminated.

Sleeve the black as blue and use as a neutral.
Use the brown as live directly.
Sleeve the grey as yellow/green and use as earth.

Connect the armour to earth at the house end or both ends according to
preference and ease.

If you are TT earthing the other end, then you don't need an earth
conductor. Just sleeve the black as blue and don't connect the grey
conductor to anythying.

Christian.