Hello
It could be that his parents were non-conformists and took little James to the nearest chapel and baptised him there.I don't know the area well and couldn't see where that may be but I can't see records on line.
The Mills family in Sourton all seem to be descended from William Mills (bapt 7.10.1733 s Of Elizabeth) and Ann Hearn who married 31.3.1766.Ann buried as Sloman or Mills 10.9.1811 age 78.
Children
Elizabeth bapt 9.7.1766 married John Dawe 13.4.1789
James (bapt as Milman) 8.11.1767 -29.11.1767
William (bapt as Milman)2.7.1769 -16.4.1829 (burial of Thurleston age 64 ) married Mary Blatchford (who was buried 11.4.1847 age 84) 16.1.1792-Children Richard 27.1.1799 and Mary 29.4.1802
James 21.6.1772 -19.3.1847 (buried as Sleeman or Mills Digaport Cottages ) married Mary Page 9.2.1796
John 26.3.1775-18.1.1778
Richard 11.1.1778 -5.6.1810 (buried as Mills or Sloman) married Mary Ellis 6.7.1802
John 22.4.1781-24.11.1867 (buried as Milman of Sourton Down) married Anne Chidley as Milman 3.1.1809.-children all Millman -William 10.9.1809,Elizabeth 14.7.1811,Richard 24.10.1813,John 17.9.1815,Anne 19.4.1818,Jane 2.4.1820,Thomas 6.4.1823,George 6.3.1824
Ann 6.3.1785
Hopefully that will give you a good start
Ciderdrinker