Whatever it is, they are not eating the flowers, just leaving them scattered around the plant, having decapitated them at the top of the stem just under the flower head.
What’s Taking Off the Heads of My Primroses?
Certified GKH Gardening Expert
There are many possible culprits, and the culprits can just snip the flowers off instead of eating them whole. This is especially true with rabbits - they cleanly cut stems/flowers off at precise, 45 degree angles from the ground. Sparrows also are known to crop primroses.