This is all I've come up with on the 1901 census for you to look at and see if there are any contenders on this list
London 1901 Census
Stephen Osborne
Age: 70
Profession: Auctioneers Assistant
London 1901 Census
Stephen Osborne
Born In: 1834
Profession: Steward Domestic
Surrey 1901 Census
Stephen Osborne
Born In: 1845
Profession: Agricultural Labourer
Kent 1901 Census
Stephen Osborne
Born In: 1849
Profession: Carman
London 1901 Census
Stephen Osborne
Born In: 1849
Profession: Deal Porter Dock Labourer
Cambridge 1901 Census
Stephen Osborne
Born In: 1850
Profession: Pattern Maker Ship
Kent 1901 Census
Stephen Osborne
Born In: 1856
Profession: Shephard
Kent 1901 Census
Stephen Osborne
Born In: 1859
Profession: General Labourer
London 1901 Census
Stephen Osborne
Born In: 1859
Profession: Builder
Bedfordshire 1901 Census
Stephen Osborne
Born In: 1861
Profession: House Painter
Hampshire 1901 Census
Stephen Osborne
Born In: 1867
Profession: Farm Labourer Fields Hand
Cornwall 1901 Census
Stephen Osborne
Born In: 1868
Profession: Clerk Draper
London 1901 Census
Stephen Osborne
Born In: 1869
Profession: Horse Keeper On Farm Ag
Suffolk 1901 Census
Stephen Osborne
Age: 18
Profession: Assistant Barman
Kent 1901 Census
Stephen Osborne
Born In: 1885
Profession: Labourer Railway Carriage Wagon Shop
Bucks 1901 Census
Stephen Osborne
Born In: 1885
Profession: Cabinet Worker
Gloucestershire 1901 Census
Stephen Osborne
Born In: 1886
Profession: Cabinet Maker
Stephen Osborn
Born In: 1842
Profession: General Labourer On Fruit Ground
Kent 1901 Census
Stephen Osborn
Born In: 1845
Profession: Pit Sawyer
Northamptonshire 1901 Census
Stephen Osborn
Born In: 1851
Profession: Brewery Labourer
Staffordshire 1901 Census
Stephen Osborn
Born In: 1852
Profession: Foreman Confectionery
London 1901 Census
Stephen Osborn
Born In: 1859
Profession: Foreman At Biscuit Factory
London 1901 Census
Stephen Osborn
Born In: 1880
Profession: Groom Domestic
Do you have Elizabeth on the 1901 census to see where she was living at the time?
also you could check 1911c to see if there are any Stephen/Steven Osborn/e's living close by
to where Kathleen's baptism took place