Thank you stanmapstone, Margaret March and wivenhoe. I thought I had already posted replies but they seem not to have reached the messageboard!
Ethel (b. Hebburn, South Shields abt 1906) is listed last on the 1911 census last, but she is also last in descending age order. Two other children are recorded as children of this marriage and these are recorded as aged 13 and 11. Wife Eleanor's (adoptive mother) age given as 51 (b. Blyth, Northumberland). Husband Francis is at his mother's house on census day and was aged about 44.
The 'adoptive' father was one of 8 sons (no daughters) and so my line of thinking is that maybe Ethel was the illegitimate daughter of one of these sons, or their offspring, and Ethel was given the mother's name. Or, as Margaret March suggested, the middle name Graham might have been the birth father's name.
I cannot find a marriage record for Francis (aka Frank on parent's death certs) and Eleanor (recorded as Eleanor A Robertson on 1901 census).
Thank you all so much for your help...any more would be welcome!
Finta