Hi Andrea and others on this thread - I have read all your posts with great interest as I too am currently researching Lucy Channer's parentage. My personal tree also starts from Arthur Wright and Lucy Channer and I have found that Lucy's father is either John or Mathew Channer.
I wrote to one of my contacts yesterday and he pointed out that there are far more details in a marriage register entry after 1837, including the fathers of the couple, but the entry for 23 Jun 1779 (if that is correct) just might say whether both parties were 'of this parish' or give their parish of residence if not. It may indicate whether Lucy was a spinster and whether the marriage was after banns or by licence. It might also be worth checking the baptisms for High Wycombe back from about 1763 just in case there is yet another Lucy CHANNER.
Matthew CHANNER married his second wife Sarah KNIBB in High Wycombe in 1705 and that she died the following year - maybe in childbirth. Ivinghoe and High Wycombe, although in the same county, were not close enough for people from the two to meet easily in that period. The nearest market towns to Ivinghoe were Aylesbury, Tring and Dunstable rather than High Wycombe. It was usual, though not mandatory, for a marriage to be in the bride's church if the couple were from different parishes, but maybe if Arthur WRIGHT's wife was indeed the Lucy CHANNER from Ivinghoe she was in domestic service in High Wycombe and so they met there. Mary WRIGHT, their first child was born/baptised 'about 1779' which might indicate a hurried marriage because she was pregnant, and also she didn't want to bring disgrace upon her family back in Ivinghoe by marrying there.
These are of course only deliberations which could turn out to be wrong as well as right.