Here is an Alfred Bedingham, in the 1881, and if you look at the 1891 that follows his middle name was ernest,
1881 England Census
about Alfred Bedingham
Name: Alfred Bedingham
Age: 3
Estimated birth year: abt 1878
Relation: son
Mother's name: Emma
Gender: Male
Where born: Soho, Middlesex, England
Civil parish: Lambeth
County/Island: London
Country: England
Street address: 186 Waterloo Rd
Education:
Employment status: View image
Registration district: Lambeth
Sub-registration district: Waterloo Road Second
ED, institution, or vessel: 15
Neighbors: View others on page
Household Members: Name Age
Alfred Bedingham 3
Emma Bedingham 24
Looks like his mother remarried by the 1891 census
1891 England Census
about Alfred Ernest Beddingham
Name: Alfred Ernest Beddingham
Age: 13
Estimated birth year: abt 1878
Relation: Stepson
Mother's name: Emma
Gender: Male
Where born: Westminster, London, England
Civil parish: Kensington
Ecclesiastical parish: St Andrew and St Phillip
County/Island: London
Country: England
Street address:
Occupation:
Condition as to marriage:
Education:
Employment status: View image
Registration district: Kensington
Sub-registration district: Kensington Town
ED, institution, or vessel: 50
Neighbors: View others on page
Household Members: Name Age
Alfred Ernest Beddingham 13
Emma Perrett 33
Emma P Perrett 8
Frances J J Perrett 5
Francess J Perrett 33
Ivy F Perrett 1
Lillie E Perrett 7
Mary A Perrett 52
If you need anything else please let me know, joyce