We put in a call to Clarks and spoke with Erica Watters, who said that while the company gets a number of questions about resoling their classic desert boots and wallabees, they don't employ an in-house cobbler for such a program. However, they do work with Resole America, a national mail-order company that will rebuild your worn out wallabees with brand new plantation crepe soles they have shipped in directly from the Clarks factory. Just print out a pre-paid label, send them off and your shoes are returned in about a week. If you're looking for someone locally, Hartland Shoe Repair in St. Paul is an old school shop that specializes in such resoling.
It's essentially a crude form of natural rubber characterized by its crinkled texture.