Think I have found Hugh Baldwin's burial in London - there is only one likely candidate:
Hugh Baldwin 58 (bc.1772), bur.31/12/1830 Chelsea Royal Hospital.
Seeing as where he was buried it seemed that he must have been a soldier at one time and indeed he was.
I found a brief service record but it has information to hopefully enable you to proceed back further:
Private Hugh Baldwin, Grenadier Guards - born Chorley, Lancashire, enlisted at age 22 and served 22 years 128 days- but in consequence of Rheumatism considered unfit for further service. He was then 44 years of age, 5'7", Dark Hair, Hazel Eyes, Fresh Complextion, By Trade a Shoe Maker.
Enlisted 14/3/1794, Discharged 19/7/1816 Whitehall.
Annette