1861 census RG9 484 folio 187
Ryarsh Kent
Edward Budd 56 Hampton, Hampshire (Havant in 1871), Married General labourer
Martha Budd 52 Tronly, Kent (Trottiscliffe in 1871), Wife Married
Thomas Budd 13 Ryarsh, Kent, Son
William Budd 8 Ryarsh, Kent, Son
John Budd 12 Ryarsh, Kent, Son
These were probably their youngest children those still at home, or still living. Edward on the 1871 census is recorded as Edward Budd senior, denoting there was an Edward Budd junior.
In Ryarsh on the 1861 census.
Folio 186
Edward Budd 27 Ryarsh, Kent, Head Married Labourer
Louisa Budd 19 Malling, Kent, Wife Married
Henry Budd 3 mths Ryarsh, Kent, Son
There is a marriage for an Edward Budd and a Martha on the IGI
EDWARD BUDD
Spouse: MARTHA KNIGHT
Marriage: 17 OCT 1833 East Malling, Kent, England
The IGI lists the children's baptisms
EdwardBudd
Christening: 14 SEP 1834 West Malling, Kent
Henry Budd
Christening: 04 SEP 1836 West Malling, Kent
MARY BUDD
Christening: 27 MAR 1842 Ryarsh, Kent
JANE ELIZABETH BUDD
Christening: 25 NOV 1839 Ryarsh, Kent
THOMAS BUDD
Christening: 30 AUG 1846 Ryarsh, Kent
WILLIAM BUDD
Christening: 10 JUN 1849 Ryarsh, Kent
JOHN BUDD
Christening: 03 APR 1853 Ryarsh, Kent
There is no Hampton in Hampshire It could be short for Southampton, but then Havant is a parish close to Portsmouth, not Southampton. I believe Portsmouth record office has indexed, certainly births from the parish records for Portsmouth and surrounding parishes so its is worth checking with them whether they have an Edward Budd baptism in Havant at about the right time. Budd is a not uncommon surname in Hampshire so there will be plenty around.
Regards
Valda