PS., The plot thickens! ... I have been working on the theory that my ancestor John Waddington who married Lydia Gibbins in 1792 was one of the children of John Wa'rr'ington (the cursive 'r' and the curly 'd' become indistinguishable) and Elizabeth Turner (1723-1785) who married 12 Oct 1744 at Medbourne. (There's another John but he doesn't convince me). Children of John & Elizabeth Warr/ddington are Henry (1745), Elizabeth (1748), Lucy (1750), Mary (1753, = Robert Sharman 28 Sep 1779), Elenor (3 July 1756, = David Smeeton 25 Sept 1786), John (18 July 1761, = Lydia Gibbins 9 Oct 1792) and Lucy (1763-1792).
The key point is that Elizabeth (1748) married Edward Bishop (m 5 Oct 1778) - all at Medbourne.
So, if these deductions are okay, there is a connection at 2nd remove through the Waddingtons in the period 1778-1792 for Bishop and Gibbins family.
Hope that might help, and would love to know if this tallies with your findings.