Just a quick update to thank everyone who replied and to let you know I've managed to resolve both problems.
Firstly, I discovered my stats are just labelled "Pulsar Infloor" which I assume was the company that supplied them. After some online investigation, I now know that they're actually made by Mohlenhoff and are the Alpha Standard model. I'm no expert but they seem to be a fairly cheap/basic stat (e.g. £21.99 on Amazon).
I did some diagnosis with a multimeter and determined that during the 20 minute pause, the stats were still receiving power but cutting off their output regardless of how high they were. All seemed to be on the same cycle, which I assume was because they were all powered up at the same moment by the main switch for the overall heating system. I temporarily hardwired the wires for one of the stats so that the stat was bypassed. The wiring centre showed that zone remained active while all the others did their pause for a minute or so. Next I bought a couple of Heatmiser DT stats (which I'd looked at anyway before any of these issues as they're much easier to control in that you can see the current room temperature). I fitted one in my kitchen and confirmed that, like bypassing the stat, if it was set high enough to be calling for heat, that zone no longer paused.
Next I went to replace my sunroom stat (the one that seemed to call for heat continuously unless I set it lower than the adjacent kitchen one). On removing the old stat, I immediately noticed that there was a bad draught coming down the conduit carrying the cables to the stat. Little did I realise the stat was being cooled from behind! I sealed around the cables at the end of the conduit, stopped the draught, fitted the stat, and left it all running for 24 hours.
I now have a kitchen and sunroom at a comfortable 20 degrees, and those zones heat when they need heat and stop when they don't. No more 20 minute cycling.
I've ordered 4 more Heatmiser DT's to replace the remaining Alpha stats. I've no reason to suspect I won't then have a system that works exactly like I'd expect it to!
Again thanks for your suggestions and advice.
Paul.