The symptoms are: Car appears to warm up normally, taking about 5-10 minutes of driving in ambient temps of about 9C to warm up to normal temp of 90C. But then the temp gauge just carries on climbing. After half an hour or so it's nudging 140 C.
 
But: The fan doesn't automatically cut in, and on opening the bonnet there's none of the associated smell or sense of an overheating engine.  Cheers, Tim

Firstly, you are not overheating. Forget that possibility. You would know it, you would smell it, your rad fan would be on continually and your rad would be overflowing.

Your water temp gauge is effected by a limited number of things.

1. Your voltage stabilizer. This items alters and maintains your 12 Volt to a 10V supply to your fuel gauge and water temp gauges. If the screw holding it at the tab looses, the
stabilizer's earth wire, held by the same screw, can lose a proper contact and the current to the gauges will jump to your alternator's output (14 +or-.5V). That will make your fuel level and water temp  jump
considerably. First, verify that the stabilizer is earth by testing the earth to the body of the stabilizer. 90% of problems are resolved here.

2. Your voltage stabilizer has failed. I have had 4 fail in the space of 2 weeks. I switched to another source from the Caerbont stabilizer (who sells to Holden, Moss, Europe, Morgan..ect etc) and resolved the problem.

You can test this item. You cannot detect the proper output from a stabilizer, but you can substitute something you know is putting out 10V. If you passed #1, get another battery and let it run down to 10V. Earth it on the car and have it feed your fuel of temp gauge directly (no stabilizer in between). If your
temps now behave, the stabilizer is blown.

BTW, I purchased the other 10V stabilizer (1.5 amp) from http://www.digikey.com #UA7810CKC They are 40 pence each rather than 8 pounds. Read this article . Try your neighbourhood Radio Shack or computer repair place.

3. The wire from the temp sender on the engine block is earthed somewhere. To test, you could simply put in another wire from the sender temporarily and loop it around to the gauge.

4. If you pass..#1-3 the sender is gone. Not unheard of. It must be replaced.

5. I have not seen this yet, but I imagine the gauge itself can go.

The key is that if it is the voltage stabilizer is abnormal in some way, both the fuel level and the water temp will be effected.