I would like to move a light switch. This will involve a new (but not
lengthy) cable run inside a stud wall, which I can do with no problems, but
what's the recommended method of attaching the new cable to the old (either
inside the present back box which can then be sealed in, or loose within the
wall cavity)?

I have to extend three earths, a joined live pair and a single live cable.

Is there a UK-approved version of the US screw-on wire-nut? Or something
similar? Many thanks.