Short answer, this statement has a few facts in it, but they are out of order, and misrepresent the history around the work, as well as where the money was coming from. In my mind, the misrepresentations are bad enough for the statement made by Matt Ridley to be completely false.
The discovery of DNA occurred in 1860, and was due to testing solutions with acids and bases, dissolving out the DNA and re-precipitating it. The man credited with this discovery is Johann Friedrich Miescher. This is important because this work happens before the discovery of X-Ray crystallography in 1912, , by Max Laue, Walter Friedrich, and Paul Knipping
For many years, DNA was considered by some to be waste product stored in the cell, thought to be obviously toxic to the rest of the cell due to the presences of a protective nucleus. In 1881, Albrecht Kossel looked at DNA closely and gave it it's current name, as well as isolating the base pairs that contain the information within a DNA molecule. His work meshed well with the work of of Gregor Mendel in the early 1860's but there were still lots of "dots not yet connected". This is important because this work happens before the discovery of X-Ray crystallography in 1912.
William Astbury, a pioneer in taking X-ray crystallography photos, did take a X-ray crystallography photo of DNA in the early 1930's, but he didn't discover much. He was looking for patterns in "long things" and his work covered a lot of "long molecules" including DNA, wool, other biological fibers, muscle, and bacteria flagella. His work contained many errors, and his success was mostly on the protein side of things, not in DNA.
Astbury's work was groundbreaking, but it wasn't perfect. His calculations sometimes had multiple atoms in the same space, an impossibility known to be impossible in his day. It was mostly the work of H. S. Taylor and Maurice Huggins that did further research showing that Astbury's repeating parts of proteins were coils, with atomic resolution (later to be name alpha-helixes) in 1943. Neither scientist seems to be funded by "Wool" as they were working at Universities (Princeton and Berkley, respectively). Oddly enough, Astbury did publish his work on DNA in 1938, but the description of the molecule was "a pile of pennies" (X-Ray Study of Thymonucleic Acid. Nature. 141 (3573): 747-748).
For the final step, Watson and Crick leveraged a number of techniques, including X-Ray crystallography in the early 1950's (1953?) to describe DNA structure. Unlike Astbury, they were primarily interested in DNA, and didn't focus on proteins (which were mostly "discovered" by then).
In short, Matt Ridley's argument is tenuous at best, and probably very false. Work on wool led to an interesting discovery, but not all at once. That work didn't really trigger the discovery of DNA's structure, even though one of the researchers took the right photograph nearly 20 years earlier than Watson and Crick.