Hi Rachel,
These are my Rouths on the 1881 census and I have Willaim and Jane's marriage certificate which shows his father was Thomas Routh and that's as far as I've gone at the moment.
1881 census
William ROUTH Head M Male 37 Malton, York, England Iron Planer
Jane E. ROUTH Wife M Female 36 Wakefield, York, England
Mary E. ROUTH Daur Female 12 Hunslet, York, England Scholar
Robert ROUTH Son Male 10 Hunslet, York, England Scholar
Henry ROUTH Son Male 4 Hunslet, York, England
Sarah A. ROUTH Daur Female 4 Hunslet, York, England
Regards
Di