Thanks for all the suggestions and guidance.
Further electrical testing hasn't found anything and all the data checks out against a similar spec car also in the workshop.
It wasn't running well when warm when I took it in but that was found to be something in the tank blocking the fuel pickup. That is cleared now but the cold running still persists.
Not seen the data from the diagnostics yet - they are 3 hours away on a good journey so not easy to pop in to see. They say they have taken data at various temps and still found nothing out of the ordinary. Think KH want to see the back of it as much as I do.
Will keep you posted.....