No single person can be pointed to as the inventor of Photoxylography – creating woodblocks cut directly from photographic images produced on the block itself. However on April 20, 1839 a photogenic drawing was cut and printed in The Mirror of Literature, Amusement, and Instruction. The method was explained “To take a Photographic Copy on Boxwood. Place the smooth side of a block of boxwood in a shallow dish or plate, containing a solution of salt, twenty grains to an once of water. When it has remained in it for about five minutes, take it out and dry it, and then put the same side in another plate containing sixty grains of nitrate of silver, dissolved in an ounce of water. After the elapse of a minute, take it out, and dry it. It will then, on exposure to light, assume a fine brown color. If it be again immersed in each solution, for a few seconds only, it will become so sensitive, as to be affected by a very slight degree of light. To obtain a drawing of a view, or a copy of a picture, &c. proceed with the prepared block, precisely according to the instructions already given for using the photographic paper. In this manner, a drawing upon a block may be most expeditiously obtained, and without the services of a draughtsman. It only needs the wood-engraver.”  After this date a number of individuals showed examples including Robert Langton in England in 1854; J. De Witt Brinckerhoff in the US in 1855, as well as Robert Price in the U.S. — whose process was commercialized in 1857. Even as late as 1861 A. Bolton, England, was credited as the inventor.
This specimen of Mr. Bolton’s new process is taken from the well-known relief of Flaxman, Deliver us from evil. Bolton had the surface of a wood block sensitized and a photograph made on it through the image thus attained. According to William Ivans it was the first reproductive wood engraving made through photographic image instead of drawing on the block by an intermediary draughtsman.  Considering the example in the Mirror in 1839, Ivans may have been incorrect.
Hanson, David A. Checklist of Photomechanical Processes and Printing, 1825-1910. , 2017. p. 105.
Ivins, William M. "Photography and the "modern" Point of View: a Speculation in the History of Taste." Metropolitan Museum Studies. 1.1 (1928): 16-24. Print p. 18
 The Mirror of Literature Amusement and Instruction. London: J. Limbird; 1823. pg. 317 May 18, 1839, no. 949
 Prints and Visual Communication By William Mills Ivins)
Ivins, William M. "Photography and the "modern" Point of View: a Speculation in the History of Taste." Metropolitan Museum Studies. 1.1 (1928): 16-24. Print
Chatto WA Jackson J Bohn HG. A Treatise on Wood Engraving Historical and Practical; with Upwards of Three Hundred Illustrations Engraved on Wood by John Jackson. 2d ed. Detroit: Gale Research; 1969
Wakeman Geoffrey. 1973. Victorian Book Illustration: The Technical Revolution. Newton Abbot: David & Charles p. 78
Gerry Beegan, “The Mechanization of the Image: Facsimile, Photography, and Fragmentation in Nineteenth-Century Wood Engraving,” Journal of Design History 8 (1995): 257-274.
Tom Gretton, “Signs for Labour-Value in Printed Pictures After the Photomechanical Revolution: Mainstream Changes and Extreme Cases around 1900,” Oxford Art Journal 28 (2005): -390.
Stephen P. Rice, “Photography in Engraving on Wood: On the road to the halftone revolution,” Common-Place 7, no. 3 (April 2007).
Nancy Carlson Schrock, “William James Linton and his Victorian History of American Wood Engraving,” in William J. Linton, American Wood Engraving: A Victorian History (Watkins Glen, N.Y., 1976).
Nancy Martha West, “Men in the Age of Mechanical Reproduction: Masculinity, Photography, and the Death of Engraving in the Nineteenth Century,” Victorian Institute Journal 27 (1999): -31.
David Woodward, “The Decline of Commercial Wood Engraving in Nineteenth-Century America,” Journal of the Printing Historical Society 10 (1974-75): -83.