So a wee update:
I decided to go onto findmypast and living in the Uckfield house (12 Walters Cottages) in 1939 does look to be my Gran Daphne, with son Hamilton, and Mother Marie Lambert. Two records are locked, guess they would be Percy Charles, husband of Daphne and my Dad Rex, will see about getting them unlocked perhaps as they are deceased.
Also in Uckfield (4 Green Sq Mount Pleasant*) in 1939 register is as you say Rosie - Anthony P Hamilton b12 Apr 1916 living in the same house as Ernestine Saunders. Anthony P Hamilton occupation is listed as Traveller (another one...). This is too tempting a link - is he the son of Marie also, born a few years after Daphne? So I have ordered his birth certificate ...
Finally in the 1960's an Anthony P Hamilton pops up in Maida Vale, just a few streets away from where Ernestine with children Ernest and Marie, are listed as living in the 1911 census. Living in the same house as Anthony P Hamilton in the 1960's is Jenni, James and JIM Morrison.
The only other ancestor I can remember from my grandmother Daphne is "Uncle Jim" who used to work a smallholding in Kent when I went to visit Granny down there in the early 70's - a coincidence?
Time for bed!
* Also in the same house as you say Rosie is the White Family (it is listed as the "White Household") James L 1890 / Susan 1904 / Charles R 1927. They are Labourer & unpaid domestic as is Ernestine.