This is a bit of a long story, so apologies. It took me a year to fix (with lots of parts swaps by Jag Coventry and some advice from an auto electrician). I learnt a lot from this forum, and others, and want to post this so if anyone else has a similar problem then they have another avenue to search.
I'm mostly over on pistonheads and was advised by some regulars from here to get help from here. I've taught myself to interpret the wiring diagrams and have learnt all about the SRS and airbag systems in the X150.

Whilst everyone told me a Check Pedestrian System message will not stop the car from starting, I can confirm it will... In certain circumstances. If the car thinks it's been in a crash and the airbags have deployed then it will tell the ECM not to run the fuel pump.

Spoiler: my issue turned out to be a broken earth on G03 (under bonnet, on wing under the engine fuse box). This grounds the pedestrian protection system. The bad earth made the car think the airbag had fired so kept the airbag light on and have me the CPS fault, and so disabled the fuel pump.
Jag Sytner gave up with the car this year and I managed to replace the crash sensors (that were throwing a code) trace the main fault, repair the earth, recode a module, clear the DTC and it's been fine ever since.

So, a sort of potted history.
March 23 the car starts but then dies like you've turn it off. Then it cranks and cranks but won't fire until it coughs into life, then dies again.
At first I was told "fuel pump".
Then it was the relay off the auxiliary fuse box.
The fault was intermittent as sometimes it would work fine, the next day it would fault. So I was confident it wasn't mechanical.
I eventually (after weeks of intermittent faults) noticed that if the fault was present then the airbag light was on and after a few mins (up to 20!!) with the ignition on the airbag would blink off and the CPS would disappear and the car would start fine.I then noticed that the car would be fine when warmed by the sun and would normally fault when cold. To me, this was like a contact somewhere making and breaking with the change in temperature.
I was also seeing 'U0151 lost connection to SRS' on my OBD scanner. The fuel pump was replaced by Jag even though I said it wasn't mechanical, but "we are Jag, we know best".

I did lots of research of the service manual and the wiring diagrams and was convinced it was related to the airbag system.When the fuel pump change didn't fix it they agreed to replace the SRS module FOC.That also didn't fix it but they said the aux fuse box wasn't putting out power to the SRS module (fuses were fine).I sourced a new fuse box from eBay but they said the problem was still there. Eventually they gave up and I got the car back on my drive.
I scanned the car with my OBD scanner and torque Pro and it said there was a VIN mismatch, so they hadn't coded the fuse box. Grrrr.

I bought a SDD system and mongoose cable and recoded the module successfully. I also replaced the impact sensors as I had seen some DTCs related to them.
The wiring diagrams said the PPS was grounded at G03 so I checked that and the nut felt loose. I took it off and the connectors were pretty dirty. On tightening the nut it sheared off. Ah ha.
I found another earth point (on the airbag mount) and connected it all back up.I cleared the codes and the CPS disappeared. For the last week the car has been perfect. I could only find a few instances of this error online. One seemed related to the aux fuse box but there was no clear follow up to say it was fixed.

I hope this post helps others in the future!
​​​This forum has been invaluable. I absolutely love the car and was so close to scrapping it last year as there seemed to be no end in sight.I'm so glad (and proud of myself) that it is now fixed.

 

Sorry, I don't know why there are no paragraphs. It was formatted fine?

Done now with the edit function.

 

You should be proud and thanks for sharing this information.
wj