Looked at my 2.5L this morning and it started at 1500rpm. There is a good reason for this. The CX-5 is the first production car to use Tri-Y (4-2-1) headers. No one has done it before because by the time exhaust gets to the catalytic converter its to cold to light the cat. Mazda solved this problem by injecting raw gas into the exhaust on cold start to quickly heat up the header and cat. The Tri-Y header is why CX-5 can run 13:1 compression on 87 octane gas and has a very low torque peak of 3250rpm. High idling on cold start is a small price to pay for best mpg, best power, and best low end torque.
Yes thank you, but we know all that, since the Skyactiv 2.0L introduced in model year 2013 CX-5 has now been out for over 2 years.
What the OP describes is not the cold start routine of our Skyactiv gasoline engines (see below). And in OP's UK market diesel engines are very common.
"On several occasions the car starts in a normal way and tick over at around 850 rpm but then, on others, it will race up to around 1800 - 2000 rpm. I reported this to the dealer and delivered the car to them for investigation only to be told all is fine. I can accept "there are no codes showing" after a diagnostic check but, nevertheless, Mazda can't give me a suitable explanation for the differing engine speeds which occur whether the engine is hot or cold."