The thirteen-pounder seems to have generally been the preferred choice as a standard pre-war. The thinking was that the cavalry would really suffer an appreciable mobility loss if the Horse Artillery were equipped with a heavier gun, whereas the infantry would simply have to fire a few extra thirteen pound shells to make up for the lighter weight of throw that a battery of 13-pounders would have compared to 18-pounders.
This probably means that the British go into the war with somewhat lighter guns firing a lighter shell. That means probably worse performance as high explosive throwers during trench warfare (the pre-war conception of artillery as highly mobile shrapnel throwers won't last into 1915). The thing is that the 13-pounder is comparable to the French 75 in terms of shell weight (or for that matter the German 7.7cm). So the British artillery will be slightly worse than OTL, but still substantially better off than the French (who almost entirely lacked the howitzers which were intended as high explosive throwers pre-war, and which Germany in particular used to great effect even during mobile warfare). The British will still have the 4.5 inch howitzer, so no change from OTL there.
The big question to my mind is whether this would help artillery ammunition production (by simplifying the number of shell types needed), or hurt it (by reducing the amount of shell production tooling equipment). Ultimately, the question is whether the British government would have recognized the value of investing in its defence industrial capacity, or whether it would have jumped on to any opportunity to save a few pence. Given that the British would have difficulties during the war since they'd been importing the acetone used for producing cordite from Germany and had never worked out alternate supply chains before the shooting started, I'm somewhat pessimistic.
