Is the Mary Jane Crow you are looking for the one recorded as "Mary A. CROW" aged 30 in the 1881 census, with John W. CROW (Son) aged 5 b.Beeston, York?

If so, the Mary Anne sent last message looks likely, if she was unmarried.

When you wrote that the father of John William born Sept 1875 was John Allen, did you mean Allen as the surname? In the 1881 census the previous household to the Crow one was for John ALLEN aged 40, b.Halifax, York, England, Miner (Coal).

Sue