There were several Robert Wilsons born in Lancaster in the right time frame (bearing in mind the age given at Robert Fred's birth), and even more Johns. Looking for two with the same mother's maiden name, I came up with this, which is interesting, given Robert Jnr's middle name:
Frederick Wilson m Elizabeth Pinch (also possibly transcribed as Finch) in Q1 1883, Lancaster, Lancashire, England.
Robert (Wilson, mmn Pinch) born Q2 1889, Lancaster
John (Wilson, mmn Pinch) born Q4 1890, Lancaster
Agnes (Wilson, mmn Pinch) born Q2 1894, Lancaster
This 1891 census return looks like them:
https://www.familysearch.org/ark:/61903/1:1:Q1JR-5MM
and this one in 1901, but without Robert:
https://www.familysearch.org/ark:/61903/1:1:X9KW-RGS