I went through the 2007 thread and cleaned this post up

Purdey Gun & Rifle Makers, The Definitive History by Donald Dallas

There was very little discussion of the barrels, and no mention of any specific named pattern nor, after the mid-1820s, if any barrels were out-sourced. I was able to establish the progression of barrels used from the excellent pictures.
In summary: prior to the 1840s all barrels were twist. In the 1840s-1860s Laminated steel and 2- and 3- Iron “Oxford” Damascus appear - asymmetric large oval scrolls



About 1870, a distinctly finer 3- and 4- iron English Best “Turkish” (smaller annular symmetric scroll) patterns appear



c. 1890, most of the barrels were Whitworth steel

p.15
Purdey began producing his own barrels in the mid-1820s.
Prior to that time, most were obtained from Charles Lancaster (‘CL’ marked) or William Fullerd (‘WF’ marked)
p. 27
Barrels made by Purdey were stamped ‘JP’ after 1826
Also Thomas Evans ‘TE’ and Thomas Parkin ‘TP’ in mid-1820s.
No further mention of any out-sourced barrels thereafter.
Aston Snr. began with Purdey's in the 1850s; his son, Harry, was also a barrel maker until 1930.

Barrel patterns in images
1818: 6b Flintlock #14 - Twist
1821: 4b Dbl percussion shotgun #287 - Twist
1844: 16b Dbl percussion rifle #3845 - Laminated
1863: 12b Dbl Bastin/Purdey slide action pinfire #6424 - Damascus ?2 rod
1864: First pattern thumb-hole pin-fire #6829 - Laminated Damascus?
1866: 12b Dbl First pattern thumb-hole #7225 - Laminated steel
1867: 40 cal. Dbl Express rifle #7464 - Large scroll 2 Iron “Oxford” Damascus
1868: 12b Second pattern thumb-hole #7745 - Large scroll 3 Iron Damascus
1869: 12b muzzle-loading shotgun #7902 - Large scroll 3 Iron Damascus
1872: 10b bar-in-wood hammer gun #8623 - First appearance of Fine small scroll “Turkish” 4 Iron Damascus
1873: 12b bar-in-wood hammer guns pair #8998 & 9000 - same Damascus as above.
c. late 1870s: Introduction of Quality A - E
Jan. 1, 1880 - Pair #10614/10615 were delivered to Mr Hunt by James Purdey 'The Younger' with The "New Whitworth Fluid Pressed Steel".
1881: Bar-in-wood hammer gun #11090 - same 4 Iron “Turkish”.
1885 Catalog - Quality A- Best Gun “The barrels of best Guns can if desired be made of Sir Joseph Whitworth & Co.s fluid pressed steel at an extra cost...”
Quality B- “Fine Damascus barrels.” No other mention of barrel material.
Crolle pattern illustrated is the same 4 Iron “Turkish”.
1884: Beesley gun #11837 - 3 Iron “Turkish”
1886: 8b hammer rifle #12371 - 3 Iron “Turkish”
c. 1890s: Guns illustrated had Whitworth steel.

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