Apprenticeship programmes for graduates are relatively new phenomena. Previously, individuals with a degree higher than a foundation degree (Level 4) were stopped from applying.
However, individuals may now, in theory, apply for apprenticeships with a degree. You may apply as long as the apprenticeship includes significant new learning. So, you won’t be able to pursue an apprenticeship in graphic design if you have a degree in it, but you may apply for a marketing apprenticeship.