My theories on why it wasn't adapted are pretty simple.
It is heavy, very heavy for a bolt action military rifle.
At this time period everyone was used to 'V' notch sights, and didn't want to use aperture sights (personally I have the same mindset myself I shoot way better with a 'V' notch), this problem was also shown in WWII with the No. 4 Mk. 1s as the already trained troops didn't want to use apertures.
The P14 was made in the States, not Britain(still very imperialistic/nationalistic mindset at this point), and they didn't use common parts as a P14 made by Winchester couldn't use Remington parts etc.
Massive stocks of Lee Enfields were on hand, which Britain already had the tooling set up for (and some of the colonies/commonwealth nations as well).
The P14 is a fantastic rifle, and can easily hold its own with contemporary rifles. It just happened at the wrong point of time in history. It is also pretty funny that the M1917 almost became the American standard rifle after they technically wrote off roughly 1 million 1903s due to poor heat treating.