That was an army-wide failing thanks to an ingrained culture in the inter-war years that was highly sceptical of having just one approved way of doing things, to the extent that even standard drills were looked on with suspicion, as it was felt that it would inhibit improvisation. This however was completely undercut by an insistence on highly regulated top-down orders during operations that tightly controlled things with a reliance on written orders that planned things step-by-step to the n-th degree. IIRC there wasn't a central School of Infantry until one was established a year or two into the war. This meant that different units such as divisions, or even brigades if independent ones, all taught their own ways of doing things and even their own spin on what little central policy there was.
Another related failing was thanks to being used on imperial policing duties the army was spread out around the globe and often didn't operate above brigade, or even battalion, level aside from a few places so that they never got to practice together as larger forces or develop the necessary staff experience to do so. The Staff College at Camberley concentrated mostly on the strategic level with very little thought given to the operational, plus they only turned out something like fifty or so graduates a year so each division in the early years of the war would be lucky to have a commander and maybe two or three other officers that had been on their staff. The regular middle-ranking officers that were expected to step up to run the newly raised units hadn't had the training or experience of staff work necessary so it created poor results. Until the British army had spent a couple of very tough years learning on the job they generally had staffs that were inadequate to the tasks they were given and were seemingly more a large grouping of brigades than effective massed divisions or corps.
As late as 1941 or 1942 I think it was someone at the War Office wrote an intelligence assessment on the
Wehrmacht. I can't remember the exact details but it basically repeated the mantra that the British army was best at improvisational thinking during operations whilst the Germans might give the
impression of such but in reality it was because they merely had a thousand and one drills they had learned and robotically followed, completely missing the whole concept of
Auftragstaktik. If it wasn't so comical it would have made you cry. I'll stop rambling on now.
Considering the up-hill battle he was facing, and the amount of time it usually takes to change an ingrained culture of many years, I don't think he could have done much different. Maybe allowed a
little more initiative, but at that point your really just arguing over degrees considering how little freedom he, and later army as a whole, seems to have been operating under. That's my opinion at least.
