Could be a lot of different things! Check very carefully between the toes (high up in the webbing) as harvest mites can cause this and look like tiny orange spots, they suck blood.
Many kinds of allergy can manifest as itchy feet. To decide what is going on here then it's a job for your vet.
You've not altered anything recently? New washing powder? New pet bedding? New flooring?
In winter when there is salt and grit on the roads this will irritate the feet and cause them to lick.