Having previously posted my doubts about the marriage of Samuel Hayes to Eliza Jane Searle in Portsea, I'm now inclined to think that may be the same family. A search of Christenings in Warrington during the period 1830-1850 throws up the following, several of which list "Eliza Jane" or "Eliza" as the mother's name, and which tally with the names and dates in the 1851 Census:
Baptism: 3 Feb 1833 St Elphin, Warrington, Lancashire, England
Elizabeth Hayes - Daur of Samuel Hayes & Jane
Abode: Townsend
Occupation: Labourer
Baptised by: T V Bayne
Register: Baptisms 1831 - 1835, Page 110, Entry 880
Source: LDS Film 1562962
Baptism: 1 Feb 1835 St Elphin, Warrington, Lancashire, England
Henry Serle Heyes - Son of Samuel Heyes & Eliza
Abode: Haydock Street
Occupation: Labourer
Baptised by: T V Bayne
Register: Baptisms 1831 - 1835, Page 257, Entry 2050
Source: LDS Film 1562962
Baptism: 29 Oct 1837 St Elphin, Warrington, Lancashire, England
Samuel Hayes - Son of Samuel Hayes & Eliza Jane
Abode: Haydock Street
Occupation: Labourer
Baptised by: T V Bayne
Register: Baptisms 1835 - 1838, Page 159, Entry 1267
Source: LDS Film 1532962
Baptism: 16 Aug 1840 St Elphin, Warrington, Lancashire, England
Henry Searle Hayes - [Child] of Samuel Hayes & Eliza
Abode: Winwick Street
Occupation: Labourer
Baptised by: Allan Wallace
Register: Baptisms 1838 - 1845, Page 131, Entry 1046
Source: LDS Film 1562963
Baptism: 27 Nov 1842 St Elphin, Warrington, Lancashire, England
Helen Fanny Hayes - [Child] of Samuel Hayes & Eliza
Abode: Winwick Street
Occupation: Hair Cutter
Baptised by: F A Bartlett
Register: Baptisms 1838 - 1845, Page 258, Entry 2061
Source: LDS Film 1562963
Baptism: 6 Apr 1845 St Elphin, Warrington, Lancashire, England
John Hayes - [Child] of Samuel Hayes & Elizabeth Jane
Abode: Turners Fold
Occupation: Labourer
Baptised by: J H Sharples
Register: Baptisms 1838 - 1845, Page 399, Entry 3186
Source: LDS Film 1562963
Baptism: 12 Dec 1847 St Paul, Warrington, Lancashire, England
Mary Heys - Daugr of Samuel Mather Heys & Eliza Jane
Abode: Turner's Fold
Occupation: Wire Drawer
Baptised by: B. M. Huntington Curate
Register: Baptisms 1831 - 1855, Page 88, Entry 707
Source: Original Parish Register
Baptism: 14 Jul 1850 St Paul, Warrington, Lancashire, England
John Hayes - Son of Samuel Hayes & Jane
Abode: Town's End
Occupation: Wire Drawer
Baptised by: B. M. Huntington Curate
Register: Baptisms 1831 - 1855, Page 121, Entry 975
Source: Original Parish Register
Sorry if Jonw65 and others had already made this discovery/connection...I'm playing catch-up here after a very busy week, and there's a lot to go through based on the discoveries in this thread.