the 15mm is the external diameter of the pipes, about as thick as your finger. 10mm is obviously smaller. Most people have 15mm copper pipe.
the 0.5" is the bit that goes into the rad - the new valves come with a new tail that you screw into the new radiator with PTFE tape on the threads.
If you are only changing one rad, you can buy a thermostatic radiator valve for a few pounds extra - these are always worth fitting, and a rad change means it is no extra work.
Thanks for getting back to me with the explanation of the dimensions.
Mine are, as you suspected 15mm.
As for pulling the plastic cap off and turning the spindle with a spanner, I've done that and unfortunately it's the spindle that goes around indefinitely.
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