Historical Context:

Unless otherwise stated the following is drawn from Drink and the Victorians by Brian Harrison.

The Beerhouse Act of 1830 was an attempt to reduce social problems casued by the excessive consumption of gin and other spirits. It abolished the beer tax, and introduced the Beerhouses and Beershops which could sell only beer. These became known as Jerry Shops.
Alcohol caused severe public health and order problems. During 1840s working people had in times of poverty a tendency to buy drink instead of food. Temperance campaigners attempted to improve diets as well as abstain from drink. The movement originated in 1828 and was always organised into a 'movement'. Teetotallers grew out of this movement during the 1830s

Various temperance organisations were established in the Glasgow area during the 1830s and 40s. (http://gdl.cdlr.strath.ac.uk/airgli/airgli0128.htm) and by 1833 Preston had become a centre of temperance movement activity https://en.wikipedia.org/wiki/Temperance_movement_in_the_United_Kingdom

A search of the British Newspaper Library reveals that Temperance Societies were established in London in 1830.

The Songs:

Bar 343 ~ Railroad to Hell was printed several times in the areas of particular Temperance activity listed above.
The Glasgow text [Glasgow University. Manuscript No. Mu23-y1:057] was printed twice by Such in London [Bodleian Library Firth c.22(123) and Harding B 11(3210)] and twice by Harkness of Preston [Bodleian Library Harding B 20(141) and Harding B 11(3209)]. The Harkness broadsides have different headlocks.

 Harding B 11(3209)].

Harding B 20(141)

 

Harkness numbered his broadsides in chronological order so it should be possible to estimate the latest date from comparison with other broadsides. Unfortunately; although Harding B 20(141) is numbered 580; the other broadside is not numbered.

The Glasgow text has several distinctly Scots words. (Dram shops, jags, and brats) which are preserved in both the Preston and London imprints and suggest that they copied the Glasgow text.

344 ~ Railway to Hell is a shorter version of Railroad to Hell and was printed in Manchester. It omits the preamble beginning "or if you will, from dissipation to poverty, and from poverty to desperation" and also three verses

Old Swiltub the Doctor and Guard of the Trains
He filches you pockets and fuddles your brains
But when he's got all form the poor silly man,
He then sends him home to do as he can,
With all his old chums, his badgers and bums,
Who sue him for money he owes in great sums

But let us not ride in the railroad to sin
Nor drink either brandy, ale, whisky, or Gin
And then we shall into heaven with joy
Where no drunken quacks can our victuals destroy
With poisonous drugs sold to use in jugs
In either their bars, their parlours, or Snugs.

And

No wonder that Pop-ticket women and Wags
Are drest up in nothing but patches and rags
Their dresses and shawls for strong liquor they'll swap.
Yes tagrag and bobtail must go to the Pop
And when this is done, away they will run
To either a Lion a Bull or a Sun.

It also changes the last lines from:

With their bonnets and hats old dresses and brats
Made up into bundles, as you may have seen Pat's

To:

With their husbands shirts, his trousers and coat
Running into the popshop to raise an odd quart.

Supporting the idea that the Glasgow imprint is the oldest.