They may exist, but I've never seen Britishproduced cheekpieces in walnut, only Canadian
. I have examples of UK cheekpieces in beech (the most common), birch (usually noticed on early conversions such as Trials & Savage rifles), & ash (usually on later war BSA Shirley rifles). Ash cheekpieces are sometimes stained quite dark, but equally are sometimes found in their pale natural wood colour. However, beech seems the most common generally. It's also difficult to be too dogmatic about it as rifles were often in service a long time & could easily have had replacement cheekpieces fitted over the years.......
From what I have read & learnt from Peter when he was researching the book the woodwork & furniture was tagged with the rifle serial number in order to ensure that it was refitted to the correct rifle once the conversion to T was completed.
P.S. Indeed H&H were not paid to swap over foresight blocks from the solid to the screw type, but in practice the requirements were relaxed when it came to foresight blocks, & many later rifles have the solid type. There is also a sub-group of 1943 rifles that bear Savage produced Mk1 (M) rear sights. This was long presumed to be because these rifles arrived at H&H as acceptable for conversion, but with the wrong rear sights. Rather than reject them a replacement 'Singer' sight was permitted. I had noted a small number of such rifles, all '43 dated, & then a while back another forummer found a documented reference to the supply of sights of Savage manufacture to H&H for this very purpose.