in basset this is often the result of yeast infection. The use of a antifungal both topical and oral can usually help. While not always yeast infenctions are often the result of a undelying problem the two most common in basset being allergies and a skin condition known as seborrhea
excessive licking is not benign it can lead to an aggrivated skin condition known as acral lick dermatitis
If there is no underlying pathology for the licking it is likely ALD which is thought to be an Obsessive compulsive disorder.
Before going the behavioral route for treatment you most rule out a medical cause. via skin scrapings etc. Keep in mind most general practicing vets are mot well versed or trained to deal with dermalogical conditions you may be better served seek a referral to a vet that specializes in dermatology.