Just to keep everyone informed I've been working on this in the chat room.
The daughter was Esther BELL 1845, wife of Robert SHORTRIDGE. She appears on census with a place of birth of Parsonby or Plumbland, with one anomalous record on the 1881 where place of birth is Lancashire.
Henry is mentioned on the marriage certificate, but I was told it said he was deceased.
I cannot find any Esther BELLs for those details with a father called Henry. If it weren't for that one mention of Henry, I would trace her back to the family of Andrew BELL and Margaret CARTY, who, incidentally, were living two doors away from the SHORTRIDGE family in 1841 and Margaret was born in Lancashire. However, some sideways thinking seems to be required in order to prove that the father was Andrew and not Henry.