Just to add the Jebber's reply, If he was recruited into the Coldstream while he was still living and working in Herefordshire or West Bromwich, it may be because the regiment was on a recruiting drive in his area at that time. He would have needed to be at least 5'8" tall to join the Guards. He would have signed up for 12 years, which at that time meant 5 years with the Colours, and 7 years in the reserve. Since the 1st and 2nd Battalions of the Coldstream went to South Africa to fight the Boers, he would naturally have been called up to serve there. As a private soldier and a fairly junior one, he is unlikely to have been granted permission to marry and so have his family 'on the strength'. However that does not mean that he was forbidden to marry and he would have suffered no detriment if he had married, other than his wife and children would not have been able to accompany him. He would still have been able to make an allotment from his pay to support his wife while he was abroad if they had married. Since it appears that they didn't marry, she would not have received a pension as a result of his death.
In fact some of his service records are available on FindMyPast. They say that he attested at Worcester on 16 Jan 1890; his occupation was labourer; he was aged 19 and 4 months and had been born in the parish of Battleburg, Bromyard, Herefordshire. He was a reservist while fighting in South Africa and his period of service there was from 3 January 1900 until his death. He died of enteric fever at Bloemfontein on either 28 or 29 May 1900 (according to 2 different records) He was buried at Bloemfontein. He was recorded as married while a reservist (so not needing leave to marry) to Ada and his two children were recorded as Albert J born 1896 and William Henry born 11 March 1900. However since he could not produce proof of his marriage his 'widow' was not paid any allowances. He was posthumously awarded the Queen's South Africa Medal with clasps for Dreifontein and Cape Colony.
Thank you! This is tremendously helpful. My delay in reply has partly been caused by looking up all the documents you so kindly directed me towards. I do use 'FindmyPast', but mostly for poring over parish registers. I hadn't realised its potential for showing original military records.
The Army's knowledge of John's alleged 'marriage' is now very clear to me - and the financial cost to my Great-Aunt Ada of not being legally married to the father of her children...
I suspect that Ada's living relatives will never know why she and John did not marry. They appear to have lived together for years, and their first child was born in his home area. Ada would have been able to visit London, while John was stationed in Chelsea Barracks. Her uncle's family lived there, and her sister and grandmother were visiting them at the time of the 1891 Census. But it is not clear if Ada ever lived in London full-time. In the Census of 1891, she was a servant in her own home area: Shropshire. She and John Perkins may have failed to organise a wedding before her child was born, and then persisted with the fiction that they were legally married...
In any case, it does appear that the Army's attitude was not a barrier to marriage. I am very grateful to you for clarifying that. And for mentioning that John was at least 5' 8" tall! That is the only information I have about his appearance, as no one known to me has ever seen a photograph. There are several of his younger brother, George, who was strikingly good-looking...
Many thanks for your very detailed and invaluable help!