1 The Church of Latter Day Saints, International Genealogical Index, www.familysearch.org/, Census 1881. Name RelationMarital StatusGenderAgeBirthplaceOccupationDisability Samuel WILLMOTT Head M Male 37 Chard, Somerset, England Lace Maker Elizabeth WILLMOTT Wife M Female 29 Beeston, Nottingham, England Mary Jane WILLMOTT Daur Female 5 Beeston, Nottingham, England Scholar George WILLMOTT Son Male 4 Beeston, Nottingham, England Scholar Elizabeth Annie WILLMOTT Daur Female 1 m Beeston, Nottingham, England Source Information: Dwelling High Street Census PlaceBeeston, Nottingham, England Family History Library Film 1341794 Public Records Office Reference RG11 Piece / Folio 3331 / 34 Page Number 8.
NOTTS-L, Gil Wilmot. Children of Samuel a Lacemaker and Elizabeth WILLMOTT of Beeston, Nottingham
Mary Jane b 25 Sep 1875 chr 4 Feb 1877 at Beeston George chr 4 Feb 1877 Elizabeth Annie chr 17 Apr 1881 at Beeston Amelia May chr 27 May 1888 at Beeston living Regent Street, Beeston Frederick John b 8 apr 1890 chr 23 Oct 1895 at Beeston living 41 Regents Street, Beeston
You will need to check the original entries for the above as they are transcripts from the Notts FHS Baptism CD.
Oddly enough I can't find a marriage on the Marriage CD at Beeston or anywhere else in Nottinghamshire and you don't say where they were married so you are going to have to buy the marriage certificate to prove parentage for Elizabeth or buy the birth certificate from Basford Register Office £7.00 + SAE to find out her parents. You will need them sooner or later to prove your line so now seems a good time!.
3 FreeBMD Online Index of BMD, England & Wales, www.freebmd.org.uk, Births Sep 1843 WILLMOTT Samuel 10 348. tentative.
4 JP (researchng Cox) 2004.
5 FreeBMD Online Index of BMD, England & Wales, www.freebmd.org.uk, Births Mar 1852 Cox Elizabeth Basford 7b 107.