The Rediffusion system carried each channel on a separate twisted pair, so subscribers had a multiway switch that connected their receiver to the pair for the channel they wanted to watch.
Nick Griffiths and Matthew Slowe both dismantled the remains of switch boxes and sent in their photos — between the two there's a fairly complete picture of what should be there.
This is the front of a switch box — it's the same size as a standard light switch, and mounted in the same sort of stand-off or recessed box on the wall, generally near where the cable entered the house. Lots of these survive in private houses and in commercial installations.
While the switch has twelve positions, most systems didn't actually provide twelve channels. Here's the back of the box Matthew found in the four-channel Thannington system. There's a multiway cable coming through the wall from the tap outside; it contains four twisted pairs. The yellow cable with a knot in it is the output from the switch; it contains just a single pair, and would have run from here to the receiver.
The switch mechanism itself is held together by a couple of screws. The contact plate (you'll see the other side in a minute) has 24 pins for incoming pairs, and two screw terminals for the outputs.
The incoming pairs were held on by little metal caps — the cable's long since gone from Nick's box, but someone helpfully left the caps behind. In this installation the multiway cable came in over the windowsill and in the bottom of the box, rather than straight through the wall as above.
The back of the faceplate has a plastic spring. You can see the notch at the left that the output cable originally left by — and the date it was made, 13th June 1983.
The spring clicks into detents on the dial...
... so that the moving contacts on the back of the dial come into contact with the right fixed contacts on the plate.
This second switch box that Matthew found had been reused as the cable entry for some regular TV aerial coax later.