We don’t actually have to rely on somewhat dated secondary sources these days, since we have the primary documents confirming Jack’s outline available now.
I don’t know whether British procurement bureaucrats were so polite as to “express a desire to standardize” on the 5” barrel.
I think they simply placed orders for that barrel length. Remember that in 1940/41 the British government was a paying customer for S&W; it wasn’t like S&W were doing them favors.
The attached summary of orders from Pate shows when the 5” barrel became standard. As we can extrapolate from research on Pate’s Colt data, these numbers represent guns ordered, not guns shipped.