First of all, let's clarify. I assume you mean the lights for the speedometer & other gauges. Is that correct?
They are supposed to light up when the parking lights or headlights are on. The brightness is controlled by turning the knob on the light switch. That adjusts a rheostat inside the light switch, and those can get dirty or go bad, so that is probably the most likely culprit, but let's check the easy stuff first.
1. Do any of the other dash lights work? (heat controls, radio, clock) Those are on the same circuit, so if any work, then the problem is with individual bulbs being burned out, or connections with the instrument cluster.
2. Do the inside dome light or the brake lights work? If yes, then you have power going into the light switch. If not, check Fuse E. They wiring diagram in the Factory Service Manual has them identified by letters, hopefully so does the fuse block under the dash. If not it will be one of the 2 fuses that are second from the end.
3. Then check Fuse F, the one on the end. That is in the circuit between the switch and the dash lights.
4. Try turning the dimmer switch back and forth. Sometimes if the rheostat is dirty or worn, there will be some spot in the rotation where it does work.
5. If that doesn't work, your best bet is either trying a different light switch, or unplugging it, and testing with a temporary jumper to bypass the switch. I'm guessing your local parts store in the UK doesn't have 50 year old American light switches in stock, and the jumper trick is a little complicated, so let us know if the easy remedies do anything first.