Hi joboy,
Good luck with Baptist records, perhaps that is where they are. I do not see them listed in the nonconformist index online although there are Adlams in Wiltshire
http://www.bmdregisters.co.uk/As I said there does not appear to be much about in the the parish churches C/E for Westbury and Dilton either. I see Adlam baptisms till 1731 in Westbury, from then just one in 1836 and starting again in 1863. I do not think it is just a lack of Adlam Records - but rather the records have not been transcribed.
There are ohh so many Adlam's buried in both Westbury and Dilton from the earliest records. I cannot see beyond 1837. Most amazingly for those times a Martha was buried in Dilton in 1772 aged 100.
Edwin does appear as Nathaniel's son in 1851 aged 6.
HO107/1842 Folio 266/267 Page 11/12
Diltons MarshADLAM Nathaniel Head 41 Mar b Westbury Hand Loom Weaver
ADLAM Fanny Wife 40 b Westbury Weavers Wife
ADLAM Joshua Son 16 b Westbury Hand Loom Weaver
ADLAM David Son 14 b Westbury Farm Lab
ADLAM Hannah M Dau 13 b Westbury
ADLAM Eliz Daub 10 b Westbury Spinner
ADLAM Mary Dau 9 Scholar
ADLAM George Son 7 b Westbury Scholar
ADLAM Edwin Son 6 b Westbury Scholar
ADLAM Walter Son 4 b Westbury Scholar
ADLAM Rosa Dau 1 b Westbury
ADLAM Prudence Dau 3 Months b Westbury
Kris