The Highway Code states that L Plates "should be removed or covered when not being driven by a learner (except on driving school vehicles)". This is because L plates are designed to show that the vehicle is being driven by a learner driver so that other drivers can be aware that the driver may be a bit more hesitant than they would otherwise expect, or more likely to make mistakes. This enables other drivers to (hopefully) be a little more patient. Although, it is not an offence to leave L Plates showing when the vehicle is being driven by a fully licensed driver, it can mis-lead everyone else. If it became very commonplace, It would also mean that L Plates would no longer signify learner drivers and so they would lose the benefits of displaying the L plates. Therefore, L plates should be removed when the vehicle is being driven by a fully licensed driver.
I've just discovered the "Text Is Beautiful" website, and its powerful analysis tools. So I put the Highway Code into it. Opposite is the related-concepts wheel it produced. Fascinating ... But it also raises some questions!