The Aisne is at the center of my research, and I feel your pain. There's not much out there.

In the grand scheme of things, overviews of the 1914 campaign tend to view the Aisne as the final stage of the Marne. To historians of the French and British armies, it represents the Entente's inability to exploit the gap between German First and Second Armies. Some trenches were dug, and the battle stabilized before both sides started swinging around the northern flank. To German historians, the Aisne often comes off as Moltke's last act and the final death of the Schlieffen Plan. He ordered his forces do dig in, and then he was out. Falkenhayn picked up and turned his attention to the northwest.

I've found one English-language book on the Aisne: Paul Kendall's The Aisne 1914: The Dawn of Trench Warfare. It's not very good, and it's not an academic history by any means. There are lots of pictures, lots of talk about operations and the movement of units, and short biographies of some of the British officers, but it breaks no new ground in terms of what it says about the battle. Yes, the Aisne was the start of trench warfare (for the British), but it doesn't drive at what the battle says about the army, its preparedness, or its ability to cope with the demands of the fighting in 1914.

If you want to know the operational side of the battle, the first volume of the British official history is still your best bet (Edmonds, Military Operations: France and Belgium 1914, volume 1). You can download it for free, I believe, on Archive.org. Though a bit stale and lacking interpretation or critical assessment, the narrative is richly detailed and dense.

If you are more interested in analysis of the battle, Nikolas Gardner, in his Trial by Fire, has a chapter on the Aisne that I'd highly recommend. Gardner addresses the operational hazards of the Aisne and how the British army adapted to the changing nature of the fighting there. It's a proper academic study that actually looks at the Aisne in the context of the army's performance and development in 1914.

Along those lines, my paper (Dykstra, "'To Dig and Burrow Like Rabbits': British Field Fortifications at the Battle of the Aisne") looks at how the British army handled the transition from mobile to trench war at the Aisne from the defensive perspective. There isn't a ton of operational info in there, but it gives a good sense of how the army prepared for defensive trench war and how its trench systems performed at the Aisne. It's due to come out in October 2018, but Chapter 2 of my MA thesis has much of the same info. You can get that here.

Other than that, the Aisne, like I said, is usually glossed over as being either an addendum to the Marne or the first stage of the Race to the Sea. Personally, and this is probably because I've spent most of my academic life studying it, I think that the Aisne was an important moment for the British army: the point at which it learned, for the first time, the true power of modern artillery, particularly howitzers. The battle also conditioned the army to large-scale entrenchment and afforded commanders the opportunity to refine their field fortification system, something that helped, to some extent, later at Ypres.

Happy to answer any follow-up questions you have.