Very interesting info from Carl Schwamberger. We are often told that the BEF was short of Artillery and MGs but from the figures it seems the BEF had roughly the same levels of equipment as the other two Armies on the Western Front. It was just that the 1914 BEF was so small about two Corps sized.
Before WW1 the British Army at home was organised somewhat to fight in Europe with 6 infantry divisions, these were about half regulars and half reserves of recent servicemen. I believe the official compliment of artillery was available for these units.
By September the 7th division was formed and in October the 8th was formed from battalions gathered from garrisons around the Empire. These were all full timers, but as scratch divisions may not have had the full compliment of artillery allocated to them in peacetime.
The 2 Indian infantry divisions which arrived in France in October had almost no artillery, so relied on the artillery of the first 6 BEF divisions.
Thus I think the artillery which was OK for 6 divisions in August was covering 8 to 10 divisions by October.