1861 census RG9 640 folio 70
7 Witton Place Portsea  Hampshire   
Thomas Hancock  25  Portsea, Hampshire,  Head Married Rope Makers Labourer
Maria Hancock  24 Portsea, Hampshire, Wife Married  
Ann E Hancock 4  Portsea, Hampshire,  Daughter  
Thomas P Hancock 2  Portsea, Hampshire,  Son  
George W Hancock  1  Portsea, Hampshire,  Son  
1871 ensus RG10 1138 folio 69
8 Lord Street Portsea  Hampshire
Thomas Hancock 35  Landport, Portsmouth Head Married Labourer Dockyard
Maria Hancock  34  Landport, Portsmouth Wife Married Staymaker
Thomas P Hancock 12 Landport, Portsmouth Son  
Jane A Hancock  9  Landport, Portsmouth Daughter      
Ellen L Hancock 8 Landport, Portsmouth Daughter     
Emily M Hancock 4  Landport, Portsmouth Daughter  
Julia E Hancock 3 Landport, Portsmouth Daughter  
Fanny Hancock  9mths  Landport, Portsmouth Daughter  
You will need to check this 1851 census entry against the details Thomas junior gives on his marriage for his father.
1851 census HO107 1659 folio 376
Swanmore Place Portsea  Hampshire   
Thos Hancock 42  Portsea, Hampshire, Head  Married Cabinet maker
Mary Hancock  35  Farlington, Hampshire, Wife Married
Thos Hancock 15  Landport, Hampshire,  Son     
Walter Hancock 2? or 12 Landport, Hampshire,  Son   
Harriett Hancock 5  Landport, Hampshire,  Daughter  
Henry Hancock 3  Landport, Hampshire, Son  
Willm Hancock 11mths  Landport, Hampshire,  Son 
James Smith 25 Landport, Hampshire, Wife's Brother Married Sawyer
Margaret Smith 25 Landport, Hampshire, Wife's Sister-in-law Married
HARRIET HANCOCK  
Birth:  26 FEB 1845    
Christening:  25 AUG 1850   Saint Marys, Portsea, Hampshire 
Father:  THOMAS HANCOCK  
Mother:  MARY  
HENRY HANCOCK  
Birth:  16 AUG 1847    
Christening:  25 AUG 1850   Saint Marys, Portsea, Hampshire, 
Father:  THOMAS HANCOCK 
Mother:  MARY  
WILLIAM HANCOCK   
Christening:  25 AUG 1850   Saint Marys, Portsea, Hampshire
Father:  THOMAS HANCOCK  
Mother:  MARY  
a possible second marriage for Thomas but this would mean either James Smith was Mary's half brother or Mary was a widow on her marriage. If it is the correct marriage you will have the details of Thomas senior's father.
THOMAS HANCOCK  
MARY FORD  
Marriage:  12 MAY 1844   Saint Marys, Portsea, Hampshire 
 
WALTER HANCOCK   
Christening:  16 MAY 1841   Saint Marys, Portsea, Hampshire, 
Father:  THOMAS HANCOCK  
Mother:  JANE  
THOMAS HANCOCK   
Christening:  06 SEP 1835   Saint Marys, Portsea, Hampshire
Father:  THOMAS HANCOCK  
Mother:  JANE  
GEORGE HANCOCK  
Christening:  18 AUG 1833   Saint Marys, Portsea, Hampshire
Father:  THOMAS HANCOCK  
Mother:  JANE  
THOMAS HANCOCK  
JANE PARSONS  
Marriage:  12 FEB 1832   Saint Thomas, Portsmouth, Hampshire 
Not the easiest census entry to find
1841 census HO107 414/7 folio 34 page 23
Crasswell Street Portsea Town  Hampshire
Thomas Hencoch 30 Hampshire Cabinet maker
Jane Hencoch 30  Hampshire
Thomas Hencoch 6  Hampshire 
Wallter Hencoch 1mth  Hampshire 
Thomas senior's second marriage should help confirm the details of his father to be sure of the baptism entry
THOMAS HANCOCK  
Birth:  21 MAY 1808    
Christening:  20 NOV 1808   Saint John, Portsea, Hampshire
Father:  THOMAS HANCOCK  
Mother:  ANN  
possible siblings
GEORGE HANCOCK  
Christening:  15 JUN 1800   Saint John, Portsea, Hampshire
Father:  THOMAS HANCOCK  
Mother:  ANN  
HARRIOT HANCOCK   
Birth:  09 AUG 1805    
Christening:  17 NOV 1805   Saint John, Portsea, Hampshire
Father:  THOMAS HANCOCK  
Mother:  ANN  
Regards
Valda