I have been interested in Sheringham Ganseys since I bought Gladys Thompson circa 2007.
By then the fine yarns needed for such fabrics were not common, and I was learning to spin yarns for Yorkshire style ganseys (e.g., 5-ply, 1,000 ypp). I spun those singles at 9 tpi and I plied those yarns at 9 ptpi. That made a nice yarn for weatherproof seaman's gear. I could spin an 8 ounce/ 500-yard hank of the 5-ply yarn in an easy 8- hour day. Spinning the yarn took about one-third as long as knitting the sweater, or hat or socks, or mittens.
I am now learning to spin "Sheringham yarns" that can be knit at 12 spi and 20 rpi. There are "swatches" everywhere. The socks I am wearing fit into that category. They are a pair, but they are knit from different yarns to test durability, and now I am getting results as one develops a hole.
I spin singles of 11,000 to 14,000 ypp at about 17 tpi. That is easy. They are lovely strong singles - I do not see such strong, durable singles on the market. Twist is expensive and yarn mills put as little twist as possible in their yarn and use "soft" as their selling point. If you are a fisherman, fishing every day, durable is more important than soft.
When plying the Yorkshire yarns, I could ply five singles of 5,600 ypp together and get a yarn of close to 1,000 ypp of grist. The math was easy!
With 17 tpi singles of 12,000 ypp, when I plied four together with 17 ptpi, I did not get a 2,700 ypp fingering that I want - it comes out closer to 900 ypp, and it knits at about 6 spi. The trick is to take the yarns fresh from spinning, and hang the singles wanted to make a yarn from, with a knot at the top and a small weight at the bottom. They will twist together to make a stable yarn. I count the twists per inch, and that is the ply twist I use to make the yarn. Counting twist is easy if I put a single of the same grist/twist/fiber, but of a different color.
It turns out that with my 12,000 ypp singles, about 4-ply twists per inch to make a yarn element and then about 4-ply twists per inch to ply the yarn elements together produce a 2x2 ply cable that makes a good fingering yarn that will knit at ~ 12 spi and 20 rpi.
I have spun such singles from various yarns ranging from fiber varying from Cotswold to Rambouillet. It works. You may not want to knit such a sweater! It is a nice yarn for socks, mittens, and hats. Because of the high twist, the yarn and the objects made from it will be both warm and durable.
By 1320, the Italians were spinning yarns that fine, and machines for plying such yarns are in Leonardo Da Vinci's notebooks. Sheringham style fabrics were then available. We have just forgotten some of those skills.
The trick is that all this is much easier if you use a differential rotation flier/bobbin assembly. Alden Amos tells how they work in his book. After the book was published, many spinner wanted such spinning wheels. Alden and Henry Clemes made and sold a bunch of such wheels, but spinners returned those wheels because they could not figure out how to use them.
For the record, using a differential rotation flier/bobbin assembly I can spin a hank (500 yards) of 12,000 ypp single in about 2 hours. I can use a standard 3" long spinning bobbin. I use flyer whorls for 17 tpi for spinning and 4 tpi whorls for plying. Plying is super fast, so I can spin a hank (88 grams) of 4-ply fingering yarn that will knit at 20 spi in an easy day of spinning. An ounce is ~ 170 yards, so the grist is ~2,800 ypp -- similar to the grist of the old Paton's Behive fingering.