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Well how did I not get THAT come up in my searches?! Thank you so much Shaun, this is great, even though it appears to rule out my man. His family were based in Cowley, Middlesex, some considerable distance from Stadhampton. 
My William Trotman enlisted into a regiment, somewhere. I’ll just have to keep searching.

The Genealogist have transcripts of burials in India, the Families of British India Society have transcripts and copies of the original registers. Are you researching this family?

Hello everyone, I may be about to break though a brick wall that’s been giving me a headache for over 20 years: what happened to my 4 x great grandfather, born in Cowley, Middlesex in 1798, who appeared to have disappeared, almost in a puff of smoke, after December 1819. I have just found a possible match, a Private of the same name (William Trotman) in the 48th Regiment of Foot, on a Convict Shop bound for NSW in 1821, followed by a burial of a man of the same name and right age, in India in 1825. Having done some online reading around the subject, including the knowledgable posts here, I’m wondering if it’s possible to take my research any further during these days of lock down. Maybe someone here can give me a new lead or two. Here’s a precise of what I know...

1798: Born Cowley, Middlesex
1815: Gets married in Clewer
1816: birth of first son
1818: birth of second son and baptism of both sons at Cowley. Gives his profession as Miller
1818: death and burial of second son (unusual name clinches ID) at Nottingham. Burial registers. Newspaper search suggests 33rd Regiment of Foot had arrived earlier in the year.
1819: in later census returns, a third son give his birthplace as Guernsey
1819: December, baptism of third son at Cowley. Father’s profession is soldier

This was where the trail went Dead until the two remaining sons turned up getting married in Reading in 1838 and 1841. No sighting of My man or his wife in any census returns but I’ve just found a woman who may have been their widowed mother, remarrying in the town where son 2 had been living and met his wife.
Recently found details that may add up to something:
1821: 16th July, A Private in the 48th, named William Trotman, is being treated for fever on the Earl St Vincent, bound for NSW
I’ve done some online research into the ship’s arrival and know roughly where the regiment were until they left for India, but no sighting of my man (and his family) during that time frame.
1825, 11 December, burial of William Trotman, aged 26, Private in the 48th Regiment of Foot, Parish of Trichinopoly St John, Tamil Nadu, India

I’ve found online information about the 48th leaving NSW for India but I don’t know when this man left or if his wife and children were with him.
I don’t want to get too excited about all this until I’ve looked at the 48th Muster Rolls. Of course, no idea when this is likely to be but if anyone has access to any further resources that could help me identify this man, including THAT BOOK about the 48th in NSW, I’d be delighted.
Thanks for reading!

Thank you Annie, and Katy for taking the time to do these searches for me!
Best wishes,
LG