I'm searching Eden family from Birmingham, Warwickshire, but do not know of any connections of mine to your Henry Charles.I have, however taken pity on you and looked up what I think is Hy Chas' family.

Henry C Eden
FBMDD 1911q2 St Pancras(1902-1977) Gtr London/London1b27 age 28 looks right for death 16 May1911.
Birth 1883 hasn't thrown up a record in FBMDB 1883 although there is Henry Charles Eden 1888q3 Islington/Gtr Lon/Lon/Middx 1b 348.

Census 1891, which would be the first to show HCE, gives, in Islington, north London, (no road name)48 'D' Block,
Harriet Eden, Head, Mar, 41, Dressmaker, born London, Holborn,
John W Eden, son, 9, Scholar,, b Islington,
Henry C do (ditto, that is, Eden),do,8,do,do
Thomas A do, do, 7, do, do,
Eliza H do, daur, 3,- do.

So, assuming this IS the right family, can we find a father?
Is the first son named after his father, who would therefore be John William Eden?

Census 1881 gives, in Islington, at 1 Evans Cottages,
John William Eden, head, Married, 41, Business Agent, born Suffolk, Bury St Edmunds,
Harriett do, Wife, Mar, 31, dressmaker, born Holborn,
Harriett Bridgeman, widow, Wife's mother, needlewoman, born Clerkenwell (south London)

To cross-check whether this is the right pair, the FBMDM gives a marriage at Kensington, London in 1874 that is not quite right. There is William John Eden, 1878q4 Kensington/London and on the same page a Harriet Hannant, Priscilla Dormer and Herbert E Meech. I checked out Meech in the C1891 and he is married to a Harriet.

A bettermatch is FBMDM 1880q3 Isln, Gtr Lon/Lon/Midx 1b 569 which has a Harriett Sheppard on the same page.

Going to the Census 1851 for Eden in Bury St Edmunds gives;-

John Eden, Head, Wdr, 42, Merchant's Clerk, born Bury.
Eliza Ann Eden, dau,13,born do.
John William do, son, 11 do.
Thos (Thomas) Woodgate do, son,9,do.
Robert Henry do, s, 7, do.
Chas Alfred do, s,5, do.
Alice Eunice do, dau, 2.

FBMDB John William Eden, 1839q4 Bury St Edmunds, Suffolk 13 576.

If this gets you further in your searches, let me know. I am going to find out if I can get a sight of the original entry for the marriage, which could confirm that the 1880 record is correct.

Whilst I don't know the details of your Edens in Canada, I have 3rd or 4th cousins that did have family in Canada although the cousins live in Australia.