They had sung his 'Tunnel Tigers' and he was carefully the significance of the chorus:
"Up with the shield and jack it, ram it""
They had sung
"Up with the shield and jacket, ram it"
Now that doesn't make sense.

Both make equal sense to me. The normal way you make a tunnel is by connecting short segments of lining after boring a few feet more hole. Why wouldn't you call the lining a "jacket"? A quick google says the word is used in exactly that way in "Tunnel Construction" [1998], edited by Messe München International, p.31.