I have always assumed that "running a mineral line" referred to the set-up for dispensing fizzy "mineral water" or carbonated drinks from an electric pump. I may be wrong. Let's face it - Betjeman was a poet, and I seldom understand anything they write.

As for the title - people who think they are cleverer than you tell us that A Shropshire Lad is a poem by A.E.Houseman. That isn't actually true. Houseman's work "A Shropshire Lad" is the name of a collection of poems, some of which have titles, but most are simply numbered by their place in the sequence.
The complete text of the book can be found at Project Gutenberg.

Quack!
GtD.