Cromwell Rd is mentioned in the 1914 directory trades section for a building contractor, that's about all.
The only mention for a club in the 1923 Kelly's Directory is,
John McNay (Sec)
Ellesmere Port, Bhead.
As far as I know, United Services Clubs were originally Gentlemen's clubs for Army & Navy officers, etc.
The building certainly looks the part.
God help us,
Don't send Jesus,
This is no place for children.