Think you should get death cert of Susan Birom, died at 86 registered 1865, her estate managed by John Martin Birom, born 1817, father listed as Birom no Christian name, mother Susan, He might be the father of John, and Hannah Slater could be the mother, she would have been a bit older than him, but these things happen!! He was single, but went on to marry, in 1845, lived in London, and died in Topsham, was a doctor.
Susan described as single on census, which might be clarified with death cert.
Only birth cerificate in 1839 in St Thomas, (which covered Topsham)gives mothers name as Connett,
Could not find a marriage of a Salter to a Connett, could have been made up.
Pity Samuel did not acknowledge him as a grandson, would have made life easier!!!
Hope this helps.