On the 1861 Census, immediately before your Lucy's parents is:
Address: ----------? -------------? -----------?
Head: Francis DRIFFIELD 41, Tile manufacturer master of, b Terrington
Wife: Lucy 22* b Flocton
Dau: Jane Ann 2* b Haxby
Dau: Hannah ??months or weeks* b Haxby
Boarder Thomas -----------? 35, unm, Farmers Servant, b Haxby
Asst: John ---------? 22, unm, Tile Manufacturers Servant, b Bradford Yks
This page, the bottom left half - where the address, names, age, relationship, gender and marital status columns are for both these DRIFFILED families - is damaged by water mark (like rain). The occupation and POB is clear. Where I have put *, I have checked them on 1871 and found their ages there, to approximate what it must say on 1861. Where it is ?, I can't make it out.
Also, enumerated up from the DRIFFIELDs is a family looks like BITTON - just interesting since your Lucy married a BRITTON or BRITTEN?
This is Francis family 1871, since I looked them up:
1871: Haxby, Yorkshire
Ref: RG10/ Piece 4742- Folio 14/ Pg 21
Address: None specific given
Head: Francis DRIFFIELD 50, Brickmaker, b Terrington
Wife: Lucy 32, b Flocton
Dau: Jane A, 12, Scholar, b Haxby
Dau: Hannah 10, Scholar, b Haxby
Dau: Esther 8, Scholar, b Haxby
Son: John 4, b Haxby
Son: Fred 2, b Haxby
Dau: Eliza 6 mths, b Haxby
And your Lucy's parents in 1871:
1871: Haxby, Yorkshire
Ref: RG10/ Piece 4742- Folio 12/ Pg 17
Address: None specific given
Head: Henry DRIFFIELD 45, Grocer & Landowner, b Terrington
Wife: Eliza 37, Grocers Wife, b Bridlington Quay
Dau: Louisa 13, Scholar, b Haxby
Dau: Emily 11, Scholar, b Haxby
Son: John H, , Scholar, b Haxby
Son; Tom 5, Scholar, b Haxby
On both the 1861 and 1871, the surname as written could easily be taken for DUFFIELD.
cheers
AMBLY