Answer:
Most definitely. Probably much like the set on a raccoon (procyon lotor), which I consider to be their closest cousins, along with pandas. Despite popular belief, Wombles are not rodents - you don't see gnaw marks on their furniture in their burrow or on the trees on Wimbledon Common. They also lack the long tail of a rodents like mice or rats.
As for proof that they have teeth?
In the episode titled "The Invisible Womble" Great Uncle Bulgaria makes mention of bramble pudding noting that "the pips get stuck between your teeth".