Bit more digging - this is a fascinating family !
National school Admission Register 1908 Beulah Road Girls School, Croydon
Phyllis Nielson d-o-b 19/02/00 father's name Henry (?) reason for leaving - left the district 3/9/09 Home address 5 Norfolk Road, Croydon
National school Admission Register 1908 Ecclesbourne Rd Girls School, Croydon
Phyllis Nielson d-o-b 19/02/00 parents' name Mrs Nielson (?)
Home address 22 Ecclesbourne Road, Croydon
Looks like Phyllis had been with her grandmother / father for some years. Could her grandfather have been Henry ?
Tried to find Elsie Maud Burgess in the same record set but no trace yet.
Have tried to trace Roland / Rowland in 1911 and the only possible so far - and its a distinct longshot is R Nelson as a inmate in a Mental Asylum in London. By the way his occupation is Upholsterer in the 1901 - checked FindMyPast and A*y to confirm.
Isn't Phyllis' entry on the 1901 census a bit odd - any ideas ?