Hi Kate
I was at Lincoln Archives this morning, and always take along a few queries from this board in case I have any spare time.
I found the marriage of Samuel Broomhead (Bach) of Beckingham (that would probably be the one just over the River Trent from Gainsborough in Nottinghamshire - not the one in Lincolnshire which is near Newark!) at All Saint's Church, Gainsborough to FANNY Harrison (Spin) of Gainsborough by Banns on 7 October 1814. Samuel signed but FANNY made her mark. Witnesses: Sarah Dickinson and the mark of Wm. Scoufield.
Sorry didn't have time to look for her baptism, but will see if the info is in Gainsbroough Library. But I did find the baptism for your other query of RUTH ATKINSON (again at All Saint's) d. of William Atkinson (Brazier) and Elizabeth, his wife on 7 March 1772.
Came across burials of two other Atkinsons: -
Thomas Atkinson - (Innholder) buried 10 October 1767 and
Penelope Atkinson buried 3 February 1766 - Widow (but obviously not Thomas'!)
Hope this helps.
Polly