The marriage of Gertrude and James Phillips lists his middle name as Thomas and in 1901 the family are living in Saltney, Flintshire with James listed as born in 1876 in Bretton? Flintshire?
In 1881 there is a James T Phillips born 1877 Bretton, Flintshire living in Saltney as below as a stepson, born presumably prior to the couples marriage.
Thomas Liversage 26 b Bretton
Mary E Liversage 20 b Hawarden, Flintshire
John Liversage 1 son b Bretton
James T Phillips 4 Step son b Bretton
If James was born pre marriage it is unlikely that a birth cert would list his father. On the FreeBMD index the only birth that I can see is in the Dec Qtr 1876 in Chester Registration District(which also covered parts of Flintshire) - James Thomas Phillips (Vol 8a Page 424)
There is a baptism of a James Thomas Phillips on 24 Dec 1876 at Church of St Mary. Broughton, Hawarden - mother listed as Mary Ellen Phillps of Bretton and no father listed. Birth listed as 10 Nov 1876.
Kay
Edit - A marriage of Thomas Liversage to Mary Ellen Phillips on 24 March 1878 lists her as 18 with father Thomas Phillips Blacksmith and his as Thomas Liversage Platelayer, so this could be Mary Ellen in 1871 (Surname transcribed as Rullops on Anc and Thomas is listed as a blacksmith)
https://familysearch.org/pal:/MM9.1.1/VBJ3-N7W