While I think the British artillery would have improved without the Second Boer War (now that I've read up a bit more, I think that they would have had roughly a BLC 15-pounder equivalent), I highly doubt they would have anything close to what they had OTL. The British really
were blind to artillery improvements in other nations before the Second Boer War:
- they had no indication that their bag guns were inferior in rate of fire to QF guns and had no plans to replace them
- they had no plans (and likely no intention) to develop recoil-absorbing guns at all (France, Germany, Russia, and the US all were developing or had already introduced such guns by then)
- they didn't see the need for heavy field guns (though to be fair, no one except Germany did until the Russo-Japanese War)
- and they were completely oblivious to the fact that their own fuses could not be set to the maximum range of their field guns
It seems that in 1899 British artillery development was disorganized at best (you can thank the Duke of Cambridge for this), and it wasn't until the Boer War that Sir Brackenbury created the Artillery Committee to develop requirements for new artillery (this produced the 18-pounder), formed from the best veterans of the Boer War. If the Boer War hadn't happened, I think that not only would those weapons not be immediately developed, but that no one would see the need for new artillery at all, which is much harder to overcome without experience. In short, the Boers already out-teched the British in 1899, I was trying to see how much farther ahead they could get (or more accurately, how much farther behind the British would fall).