On the 1891 census your James W has his place of birth given as Lincolnshire. I checked the earlier censuses to see whether there was a James Chambers born roughly 1864 in Lincolnshire and found one. His father was a station master on the 1871 census. However this James could be followed on all the subsequent censuses up to 1901 (including his marriage and children) - so he isn't yours, though his occupation was in the railway industry, like his father. The other coincidence with this James was that though his parents were born in Lincolnshire, on the 1871 Lincolnshire census he had a younger brother born 'Whittledea' Cambridgeshire. Both brothers and parents were in Lincolnshire on the 1871 census. I could find no other James Chambers of the right age on censuses earlier than 1891, and who was born in Lincolnshire.
Have you searched the period around 1864 for the birth registration of a James William Chambers either in Cambridgeshire or Lincolnshire. How many are there between 1863 and 1865? Is it to many to chance a birth certificate?
By the way Maud M was actually missed off the 1891 census index, though she was there on the page itself with her parents. Her elder sister Martha was misindexed. Whoever had typed the name into the index had inadvertantly typed Martha into the surname section and Chambers into the first name section, so no search for Martha Chambers could have found her.
Regards
Valda