That’s a real good point. You really don’t hear a thing about CAS by the British even in the initial Italian engagements.
That’s not the worst of it. The Brits consistently spread their armor out all over creation. Their armored divisions are never concentrated, their brigades are seldom within supporting distance if each other. The brigade seems to be their basic maneuver unit. “Penny Packets”, they called them. You can see it on today’s map.
That allowed the Germans, for much of the next two years, to defeat numerically superior British tank forces by attacking them in detail. Or as someone who would probably have been just as home on a tank as he was on a horse, they “got there fust’est with the mostest”.