Well, I just got the car back from its first service - which I have to say Perkins delivered without blemish - full software updates and every query looked-into. The TPMS was high on the 'niggle' list, and their response was exactly as has been proposed by others above - but moreso. They said that the problem occurs when pressures are set too low (I had checked all mine at 250 kpa immediately before the service). They further advise for all Trophy and X-Power cars with the 18"+ wheel sizes to pump them up to 3 bar (300 kpa) or 43.5 psi all round - which they say that they did ...
... However; there is still a small issue with this in that although the car now shows 300 kpa on the screen, I have since checked the tyres to see if my pump agreed - and it didn't - and neither did the pump supplied in the car's tyre repair kit, nor two manual gauges that I also tried ... all agreeing at 285 kpa / 41.5 bar. So I suspect that maybe the garage used either the car's screen for measurement (unlikely and probably impossible with the car motionless), or their own pump gauge is wrong. After four separate equipment tests, one tends to suspect that the car's TPMS reads about 5% high (in my case).
Either way, at least the TPMS hasn't so far faltered since is it stands, so I will leave well alone and just monitor it. The other more important factor from all this is that the service report showed that all the tyres were also 0.5 mm more worn (after only 4,500 miles) along both edges - most likely due to underinflation - so hopefully that should also at least get no worse now.
