Since the 1921 census says Henry/Harry SMITH was born Lower Boddington, Northanmptonshire, this looks like a likely baptism:
Henry SMITH bap 21 Oct 1889 at Boddington, parents William (labourer) and Mary Ann.
Probable birth registration Sept qtr 1889 Banbury (3a/891) mmn ADKINS. (Lower Boddington is in the Banbury Registration District)
They are relatively easy to find on the censuses, other children to William and Mary Ann SMITH of Lower Boddington also have mmn ADKINS/ATKINS. William is born c1864 Lower Boddington.
There is a William SMITH and Mary Ann ADKINS on the same page Jun qtr 1882 Banbury (3a/1265).