[Fiji Hill]

[Vera Lynn had] sung with the Charlie Kunz orchestra and had made a solo record of a leaden novelty called "Up The Wooden Hill To Bedfordshire".

Up the Wooden Hill to Bedfordshire--Vera Lynn (1936)

"Bedfordshire" means bed and the "wooden hill" is a stairwell. Not sure what a GG is.

[Songcraft]

"Gee-gee" is a UK child's name for "horse", according to this source.   (The kid in this song must have rode up the wooden hill on daddy's back.)

[ScaniaBoy]

Bedfordshire is a small county in east England situated between London and Cambridge. (Image with wooden hill.)

I don't know what GG means (Governor General does not quite fit), but the first time she sings about her father it sounds like he is the old GP (general practitioner). The second time I also hear "GG", but could that have been a mistake? No possibilities to make a digital correction in those days.