Thank you MaxD for finding an explanation about the NA ref.i found, I was going round in circles

I don't think that John appear would appear in it as image 2 mentions "claiming Medals under the General Order dated 1st June 18147" I think it is images of this medal list,
https://www.forces-war-records.co.uk/medals/military-general-service-medalJohn died in 1829.
But I think that the idea of John BLACK serving in the Peninsular War is a good possibility, it might explain why there is a gap in the children's births between 1808 to 1815. I wonder if Ann went with him and had other children abroad?
Do you know where the Sappers and Miners pension records are? The nearest thing I can see is the "War Office and predecessors: Engineers Muster Books and Pay Lists" which refers to the "The Royal Corps of Sappers and Miners," bit seems to be a huge amount of different regiments and companies etc. I have no idea how to search it to find John BLACK or if that is even possible without going to the NA

If John worked for the East India Company after leaving the British Army couldn't he receive his Army pension when he left?
You sound more knowledgeable about military records that I am, I'm on a steep learning curve

The John BLACK with the Royal Artillery record could easily be a different one but my curiosity would make me check

Regards,
Daisy