According to Karl Dallas' Cruel Wars the tune is Musselburgh Fair, and I give his version below.

He has some minor textual differences with Terry's version, different verse order and 1 extra verse. The version there has:

Now my boys if you will listen...
So I packed my bag at the double...
When we reached the railway station...
We were all packed in the corridor...

For eleven long hours we stood there and watched the fields go by
We were packed so close we couldn't even smoke and that's no lie.
And all the time the Yanks talked big and boasted they were tops
And wrestled with their judies now and then between the stops.

At last the train reached Manchester...
I humped my pack upon my back...
I let myself in quietly...
For a moment I stood speechless...
And then I waded in, my boys...
This geezer looked me over...
My story's nearly over...

Mick

---

X: 1
T:Second Front Song
M:C
L:1/4
C:Words: Ewan MacColl Tune:Musselburgh Fair
S:Dallas - The Cruel Wars
K:DDor
A/ A/|A A A A|A A2 A|A A/ A/ A< E|C3
w:Now my boys if you will lis-ten I'll sing you a lit-tle song
G|G G G> A|G G2 G|D E F G|A3
w:So sit you down a-while here I won't de-tain you long
A/ A/|D D D D|d d d d|c B A G|c3
w:I was se-ving in the in-fan-try was told I would re-ceive
D|F F E E|D E F G|A G F E |D3||
w:With all the oth-er blokes a week-end's em-bar-ka-tion leave
A|A2 D A|A2 D A/ A/|A/ A/ G2 E|C3
w:It's here chums, it's here chums, It's the Se-sond Front for you
F|G> G G< G|G/ G G/ G G/ G/|D E F G|A3
w:In spite of their old At-lan-tic Wall we're the boys to see it through
A|D D D D| d/ d/ d z d|c B A F|c3
w:It won't take long to fin-ish it when we have got their range
E|F F/ F/ E E|D E F G|A G F E|D3||
w:And then we can all go home and live like hu-mans for a change.