Success.
As you said, Ellen Feltham did die in 1947 and Henry James in 1960:
Ellen Feltham Dec.qtr. 1947 Hull aged 72
Henry J. Feltham Dec. qtr. 1960 Hemel Hempstead (Herts) aged 92.
Henry J. Feltham remarried Jun. qtr. 1952 Holderness (Yorks) to CLARA OAKLEY. So, it would seem he maybe married his first wifes sister. Didn't find death of second wife but I was looking for a Jane anyway so will have another look later.
From his death Henry James Feltham was bc.1868 so then looked for his birth entry and there is only one:
Henry James Feltham Jun.qtr. 1869 Shoreditch (IGI shows he was born 30/4/1869 and baptised 11/7/1869 St. John the Baptist, Shoreditch son of Henry Francis Feltham and Caroline).
Then looked at 1871 census and found him:
1871 - 57 Herbert Street, St. Leonard, Shoreditch.
Henry Francis Feltham 27 Tailor b. Islington, Middx.
Caroline Feltham 22 b. Kent Road, Surrey
Henry James Feltham 1 b. Hoxton, Middx.
George Francis Feltham 4 mos. ditto
Ref. RG10 446 9 11
Caroline Feltham bc.1849 d. Mar.qtr. 1873 Camberwell.
Eventually found the 2 boys in 1881 although this time birthplaces given as Southwark - however, I suspect they may have ended up in an institution in Southwark after their mother died and then sent to the Industrial School, hence birthplaces given as Southwark:
1881 - Middlesex County Industrial School, Feltham, Middlesex
Includes:
Henry Feltham Inmate 11 Detained under Industrial Schools Act b. Southwark
George Feltham Inmate 10 ditto ditto
(the latter's birth registered Dec.qtr.1870 Shoreditch).
Haven't found either in 1891 and 1901 but we know that at least Henry was a Mariner and likely to have been at sea.
However, didn't like what I found next and although he's your ancestor have decided I don't like Henry Francis Feltham.
First I found his marriage to Caroline Joyce Mar.qtr.1867 Marylebone. Assuming (something one should never do) that Henry Francis had died too I then searched for his death but there was nothing right up to 1920. In the end did a search in the marriages and found that he re-married to:
Adeline Margaret Austin Dec.qtr. 1875 Camberwell.
1881 Census - 250 Old Ford Road, Bethnal Green
Henry Feltham 37 Tailor B. Islington, Middx.
Adelina Feltham 30 b. Kingsland, Middx.
Sydney Feltham 9 b. Hackney, Middx.
Adelina Feltham 4 b. Old Ford Road, Kent
Bertha Feltham 3 ditto
Gertrude Feltham 2 ditto
Frederick Feltham 7 mos. b. Leytonstone, Essex
RG11 0416 68 10
1891 - 9 Albert Terrace, Carlyle Road, Little Ilford, Essex
Henry Feltham 47 Tailor's journeyman b. Islington, Middx.
Adeline Feltham 34 (??) b. Kingsland, Middx.
Adeline Feltham 14 Scholar b. Old Kent Road, Surrey
Bertha Feltham 13 ditto b. Leytonstone, Essex
Gertrude Feltham 12 ditto ditto
Frederick Feltham 10 ditto b. Hackney, Middx.
Beatrice Feltham 5 ditto b. Plymouth, Devon
Mable Feltham 3 b. Bishops Stortford, Herts.
Harvey Feltham 1 b. Manor Park, Essex.
ref. RG12 - 1342 - 39 - 25
The third son, Sydney, born from the 1st marriage also marries in Hull in 1900 - Sydney Herbert Feltham married to either Edith Blackborow or Mary Chapman Mar.1900 Hull.
Sydney Herbert F. birth regd Mar.qtr.1872 Camberwell
children from 2nd marriage:
Adeline Frances Jun.qtr. 1876 Camberwell
Bertha Frances Dec.qtr.1877 West Ham
Gertrude Frances Mar.qtr. 1879 West Ham
Frederick Francis Dec.qtr. 1880 Hackney
Beatrice Frances Dec.qtr. 1885 Plymouth
Mabel Francis Sept.qtr. 1887 Bishops Stortford
Harvey bc. 1890 - cannot find birth entry
New Town, Bishops Stortford (HO107 1706 426 59)
Annette