Hi, Lesley,
It sounds like you already have the following info, but here it is anyway. I also cannot find a birth record for Edward. My guess is his father's name was Robert.
There is an Edward Phillips on the 1841 census in Bath, Somerset, England as follows:
Harriet Phillip 35
Edward Phillip 35 laborer born in Somerset
Sarah Phillip 9
Harriet Phillip 7
Jane Phillip 5
Caroline Phillip 3
There is an Edward Phillips on the 1851 census in Bath, Somerset, England as follows:
Edward Phillips 47
Harriet Phillips 48
Harriet Phillips 18
Caroline Phillips 13
Robert Phillips 9
George Phillips 7
Mary Ann Phillips 4
Edward John Phillips 1
There is a Robert Phillips on the 1861 census in Bath, Somerset, England as follows:
Harriett Phillips 57 head
Harriett Phillips 27 daughter
Jane Phillips 25 daughter
Caroline Phillips 22 daughter
Robert Phillips 19 son
George Phillips 16 son
Edward J Phillips 11 son
There is a Robert Phillips on the 1871 census in Bath, Somerset, England, as follows:
Robert Phillips 29
Caroline Phillips 23
Alice Phillips 3
Ada Phillips 1 Year, 7 Months
There is a Robert Phillips on the 1881 census in Bath, Somerset, England, as follows:
Robert Phillips 38 head
Caroline Phillips 35 wife
Harriet A. Phillips 12 daughter
Ada Anne Phillips 10 daughter
Edward C. Phillips 8 son
Walter R. Phillips 6 son
Albert H. Phillips 3 son
Arthur G. Phillips 1 son
Caroline Phillips 42 sister
His occupation was painter and plasterer. In 1891, the family was living in Bath, Somerset, England as follows:
Robert Phillips 49
Caroline Phillips 46
Ada Phillips 21
Edward Phillips 19
Walter Phillips 16
Albert Phillips 13
Arthur Phillips 11
Alfred Phillips 7
Kate Phillips 9
William Phillips 4