Thank you both, RayB and Tup1, for taking out your own time to look .
It remains a mystery as to where the idea that an Elizabeth Polhill married this Richard Reddish originated. I would love it to be so but not without records proof.
I did spend time looking again at the Castle Bytham parish records book via the LincsToPast website.
I did see 3 baptisms whose father was a Richard Reddish. However there is no mention of his wife's name at all.
1 - Elizabeth baptised 9 March 1717
2 - Richard 25 July 1725
3 - Mary 8 November 1721.
Looking again at the IGI Family search, the records actually don't mention the Mother's name at all .
So , not only am I unable to independently confirm the popular notion that his wife was an Elizabeth Polhill ( descendant of Oliver Cromwell ), I am also now unable to state her first name was Elizabeth.

If Richard Reddish needed to be married by license for some reason, wouldn't he have done this in Lincolnshire and not Nottinghamshire? This is in reference to the marriage I found online for an Richard Reddish who married an Elizabeth Crumwell.
When I look at FindMyPast I can also see a Lincs marriage record of 25 Feb 1716 where a Richard Reddish married a Mary Derry. - This would be a place called SKillington, Beltisloe. Is this place close to Castle Bytham at all?
